lectures/07_linear-models.ipynb

{
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   "source": [
    "![](img/330-banner.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "# Lecture 7: Linear Models\n",
    "\n",
    "\n",
    "UBC 2022 Summer\n",
    "\n",
    "Instructor: Mehrdad Oveisi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import sys\n",
    "\n",
    "sys.path.append(\"code/.\")\n",
    "\n",
    "import IPython\n",
    "import ipywidgets as widgets\n",
    "import matplotlib.pyplot as plt\n",
    "import mglearn\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from IPython.display import HTML, display\n",
    "from ipywidgets import interact, interactive\n",
    "from plotting_functions import *\n",
    "from sklearn.dummy import DummyClassifier\n",
    "from sklearn.feature_extraction.text import CountVectorizer, TfidfVectorizer\n",
    "from sklearn.impute import SimpleImputer\n",
    "from sklearn.model_selection import cross_val_score, cross_validate, train_test_split\n",
    "from sklearn.neighbors import KNeighborsClassifier, KNeighborsRegressor\n",
    "from sklearn.pipeline import Pipeline, make_pipeline\n",
    "from sklearn.preprocessing import OneHotEncoder, StandardScaler\n",
    "from sklearn.svm import SVC\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from utils import *\n",
    "\n",
    "%matplotlib inline\n",
    "pd.set_option(\"display.max_colwidth\", 200)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Lecture plan for today\n",
    "\n",
    "- Announcements (~1 min)\n",
    "- Q&A and exercises on pre-watched video 7.1 (~10 mins) \n",
    "- Live explanation: Interpreting linear regression coefficients (~10 mins)\n",
    "- Q&A and exercises on pre-watched video 7.2 and 7.3 (~15 mins) \n",
    "- Break (~5 mins)\n",
    "- Live demo: Linear SVM and interpreting logistic regression coefficients (~30 mins)\n",
    "- Summary and wrap up (~5 mins)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Announcements\n",
    "\n",
    "- Homework 4 will be released today (Due date: Oct 12th because Monday, Oct 11th is a holiday.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "## Learning outcomes\n",
    "\n",
    "From this lecture, students are expected to be able to: \n",
    "\n",
    "- Explain the general intuition behind linear models;\n",
    "- Explain how `predict` works for linear regression;\n",
    "- Use `scikit-learn`'s `Ridge` model; \n",
    "- Demonstrate how the `alpha` hyperparameter of `Ridge` is related to the fundamental tradeoff; \n",
    "- Explain the difference between linear regression and logistic regression;   \n",
    "- Use `scikit-learn`'s `LogisticRegression` model and `predict_proba` to get probability scores\n",
    "- Explain the advantages of getting probability scores instead of hard predictions during classification; \n",
    "- Broadly describe linear SVMs \n",
    "- Explain how can you interpret model predictions using coefficients learned by a linear model; \n",
    "- Explain the advantages and limitations of linear classifiers \n",
    "- Carry out multi-class classification using OVR and OVO strategies. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "<br><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Linear models [[video](https://youtu.be/HXd1U2q4VFA)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Linear models** is a fundamental and widely used class of models. They are called **linear** because they make a prediction using a **linear function** of the input features.  \n",
    "\n",
    "We will talk about three linear models: \n",
    "- Linear regression \n",
    "- Logistic regression\n",
    "- Linear SVM (brief mention)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Linear regression \n",
    "\n",
    "- A very popular statistical model and has a long history.  \n",
    "- Imagine a hypothetical regression problem of predicting weight of a snake given its length. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>length</th>\n",
       "      <th>weight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>73</th>\n",
       "      <td>1.489130</td>\n",
       "      <td>10.507995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>53</th>\n",
       "      <td>1.073233</td>\n",
       "      <td>7.658047</td>\n",
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       "      <th>49</th>\n",
       "      <td>0.984653</td>\n",
       "      <td>9.731572</td>\n",
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       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0.484937</td>\n",
       "      <td>3.016555</td>\n",
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      "text/plain": [
       "      length     weight\n",
       "73  1.489130  10.507995\n",
       "53  1.073233   7.658047\n",
       "80  1.622709   9.748797\n",
       "49  0.984653   9.731572\n",
       "23  0.484937   3.016555"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(7)\n",
    "n = 100\n",
    "X_1 = np.linspace(0, 2, n) + np.random.randn(n) * 0.01\n",
    "X = pd.DataFrame(X_1[:, None], columns=[\"length\"])\n",
    "\n",
    "y = abs(np.random.randn(n, 1)) * 3 + X_1[:, None] * 5 + 0.2\n",
    "y = pd.DataFrame(y, columns=[\"weight\"])\n",
    "snakes_df = pd.concat([X, y], axis=1)\n",
    "train_df, test_df = train_test_split(snakes_df, test_size=0.2, random_state=77)\n",
    "\n",
    "X_train = train_df[[\"length\"]]\n",
    "y_train = train_df[\"weight\"]\n",
    "X_test = test_df[[\"length\"]]\n",
    "y_test = test_df[\"weight\"]\n",
    "train_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's visualize the hypothetical snake data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_train, y_train, \".\", markersize=10)\n",
    "plt.xlabel(\"length\")\n",
    "plt.ylabel(\"weight (target)\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's plot a linear regression model on this dataset. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "grid = np.linspace(min(X_train.to_numpy())[0], max(X_train.to_numpy())[0], 1000)\n",
    "grid = grid.reshape(-1, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/kvarada/opt/miniconda3/envs/571/lib/python3.9/site-packages/sklearn/base.py:441: UserWarning: X does not have valid feature names, but Ridge was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "\n",
    "r = Ridge()\n",
    "r.fit(X_train, y_train)\n",
    "plt.plot(X_train, y_train, \".\", markersize=10)\n",
    "plt.plot(grid, r.predict(grid))\n",
    "plt.grid(True)\n",
    "plt.xlabel(\"length\")\n",
    "plt.ylabel(\"weight (target)\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**The orange line is the learned linear model.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Prediction of linear regression\n",
    "\n",
    "- Given a snake length, we can use the model above to predict the target (i.e., the weight of the snake). \n",
    "- The prediction will be the corresponding weight on the orange line. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/kvarada/opt/miniconda3/envs/571/lib/python3.9/site-packages/sklearn/base.py:441: UserWarning: X does not have valid feature names, but Ridge was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([6.20683258])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "snake_length = 0.75\n",
    "r.predict([[snake_length]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### What are we exactly learning? \n",
    "\n",
    "- The model above is a line, which can be represented with a slope (i.e., coefficient or weight) and an intercept. \n",
    "- For the above model, we can access the slope (i.e., coefficient or weight) and the intercept using `coef_` and `intercept_`, respectively. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5.26370005])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r.coef_  # r is our linear regression object"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.2590575478171857"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r.intercept_  # r is our linear regression object"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### How are we making predictions? \n",
    "- Given a feature value $x_1$ and learned coefficient $w_1$ and intercept $b$, we can get the prediction $\\hat{y}$ with the following formula:\n",
    "$$\\hat{y} = w_1x_1 + b$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6.20683258])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prediction = snake_length * r.coef_ + r.intercept_\n",
    "prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/kvarada/opt/miniconda3/envs/571/lib/python3.9/site-packages/sklearn/base.py:441: UserWarning: X does not have valid feature names, but Ridge was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([6.20683258])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r.predict([[snake_length]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Great! Now we exactly know how the model is making the prediction. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Generalizing to more features\n",
    "For more features, the model is a higher dimensional hyperplane and the general prediction formula looks as follows: \n",
    "\n",
    "$\\hat{y} =$ <font color=\"red\">$w_1$</font> <font color=\"blue\">$x_1$ </font> $+ \\dots +$ <font color=\"red\">$w_d$</font> <font color=\"blue\">$x_d$</font> + <font  color=\"green\"> $b$</font>\n",
    "\n",
    "where, \n",
    "- <font  color=\"blue\"> ($x_1, \\dots, x_d$) are input features </font>\n",
    "- <font  color=\"red\"> ($w_1, \\dots, w_d$) are coefficients or weights </font> (learned from the data)\n",
    "- <font  color=\"green\"> $b$ is the bias which can be used to offset your hyperplane </font> (learned from the data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Example \n",
    "\n",
    "- Suppose these are the coefficients learned by a linear regression model on a hypothetical housing price prediction dataset. \n",
    "\n",
    "| Feature | Learned coefficient |\n",
    "|--------------------|---------------------:|\n",
    "| Bedrooms | 0.20 |\n",
    "| Bathrooms| 0.11 |\n",
    "| Square Footage | 0.002 |\n",
    "| Age | -0.02 |\n",
    "\n",
    "- Now given a new example, the target will be predicted as follows: \n",
    "| Bedrooms | Bathrooms | Square Footage | Age |\n",
    "|--------------------|---------------------|----------------|-----| \n",
    "| 3                  | 2                   | 1875           | 66  |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\hat{y} = w_1x_1 + w_2x_2 + w_3x_3 + w_4x_4 + b$$\n",
    "\n",
    "$$\\text{predicted price}=  0.20 \\times 3 + 0.11 \\times 2 + 0.002 \\times 1875 + (-0.02) \\times 66 + b$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "When we call `fit`, a coefficient or weight is learned for each feature which tells us the role of that feature in prediction. These coefficients are learned from the training data.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "```{important}\n",
    "In linear models for regression, the model is a line for a single feature, a plane for two features, and a hyperplane for higher dimensions. We are not yet ready to discuss how does linear regression learn these coefficients and intercept.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### `Ridge`\n",
    "\n",
    "- `scikit-learn` has a model called `LinearRegression` for linear regression. \n",
    "- But if we use this \"vanilla\" version of linear regression, it may result in large coefficients and unexpected results. \n",
    "- So instead of using `LinearRegression`, we will always use another linear model called `Ridge`, which is a linear regression model with a complexity hyperparameter `alpha`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression  # DO NOT USE IT\n",
    "from sklearn.linear_model import Ridge  # USE THIS INSTEAD"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use `sklearn`'s built in regression dataset, the Boston Housing dataset. The task associated with this dataset is to predict the median value of homes in several Boston neighborhoods in the 1970s, using information such as crime rate in the neighbourhood, average number of rooms, proximity to the Charles River, highway accessibility, and so on."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/kvarada/opt/miniconda3/envs/571/lib/python3.9/site-packages/sklearn/utils/deprecation.py:87: FutureWarning: Function load_boston is deprecated; `load_boston` is deprecated in 1.0 and will be removed in 1.2.\n",
      "\n",
      "    The Boston housing prices dataset has an ethical problem. You can refer to\n",
      "    the documentation of this function for further details.\n",
      "\n",
      "    The scikit-learn maintainers therefore strongly discourage the use of this\n",
      "    dataset unless the purpose of the code is to study and educate about\n",
      "    ethical issues in data science and machine learning.\n",
      "\n",
      "    In this case special case, you can fetch the dataset from the original\n",
      "    source::\n",
      "\n",
      "        import pandas as pd\n",
      "        import numpy as np\n",
      "\n",
      "\n",
      "        data_url = \"http://lib.stat.cmu.edu/datasets/boston\"\n",
      "        raw_df = pd.read_csv(data_url, sep=\"\\s+\", skiprows=22, header=None)\n",
      "        data = np.hstack([raw_df.values[::2, :], raw_df.values[1::2, :2]])\n",
      "        target = raw_df.values[1::2, 2]\n",
      "\n",
      "    Alternative datasets include the California housing dataset (i.e.\n",
      "    func:`~sklearn.datasets.fetch_california_housing`) and the Ames housing\n",
      "    dataset. You can load the datasets as follows:\n",
      "\n",
      "        from sklearn.datasets import fetch_california_housing\n",
      "        housing = fetch_california_housing()\n",
      "\n",
      "    for the California housing dataset and:\n",
      "\n",
      "        from sklearn.datasets import fetch_openml\n",
      "        housing = fetch_openml(name=\"house_prices\", as_frame=True)\n",
      "\n",
      "    for the Ames housing dataset.\n",
      "    \n",
      "  warnings.warn(msg, category=FutureWarning)\n"
     ]
    },
    {
     "data": {
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       "      <th></th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "      <td>0.448</td>\n",
       "      <td>5.682</td>\n",
       "      <td>33.8</td>\n",
       "      <td>5.1004</td>\n",
       "      <td>3.0</td>\n",
       "      <td>233.0</td>\n",
       "      <td>17.9</td>\n",
       "      <td>396.90</td>\n",
       "      <td>10.21</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.09378</td>\n",
       "      <td>12.5</td>\n",
       "      <td>7.87</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.524</td>\n",
       "      <td>5.889</td>\n",
       "      <td>39.0</td>\n",
       "      <td>5.4509</td>\n",
       "      <td>5.0</td>\n",
       "      <td>311.0</td>\n",
       "      <td>15.2</td>\n",
       "      <td>390.50</td>\n",
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       "    <tr>\n",
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       "      <td>300.0</td>\n",
       "      <td>16.6</td>\n",
       "      <td>383.78</td>\n",
       "      <td>7.37</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.01432</td>\n",
       "      <td>100.0</td>\n",
       "      <td>1.32</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.411</td>\n",
       "      <td>6.816</td>\n",
       "      <td>40.5</td>\n",
       "      <td>8.3248</td>\n",
       "      <td>5.0</td>\n",
       "      <td>256.0</td>\n",
       "      <td>15.1</td>\n",
       "      <td>392.90</td>\n",
       "      <td>3.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "      <td>...</td>\n",
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       "      <th>399</th>\n",
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       "      <td>0.0</td>\n",
       "      <td>6.20</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.507</td>\n",
       "      <td>7.358</td>\n",
       "      <td>71.6</td>\n",
       "      <td>4.1480</td>\n",
       "      <td>8.0</td>\n",
       "      <td>307.0</td>\n",
       "      <td>17.4</td>\n",
       "      <td>390.07</td>\n",
       "      <td>4.73</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>400</th>\n",
       "      <td>23.64820</td>\n",
       "      <td>0.0</td>\n",
       "      <td>18.10</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.671</td>\n",
       "      <td>6.380</td>\n",
       "      <td>96.2</td>\n",
       "      <td>1.3861</td>\n",
       "      <td>24.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>20.2</td>\n",
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       "      <td>32.0</td>\n",
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       "      <td>1.0</td>\n",
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       "      <td>16.4</td>\n",
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       "      <td>0.605</td>\n",
       "      <td>6.250</td>\n",
       "      <td>92.6</td>\n",
       "      <td>1.7984</td>\n",
       "      <td>5.0</td>\n",
       "      <td>403.0</td>\n",
       "      <td>14.7</td>\n",
       "      <td>338.92</td>\n",
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       "      <td>0.713</td>\n",
       "      <td>6.301</td>\n",
       "      <td>83.7</td>\n",
       "      <td>2.7831</td>\n",
       "      <td>24.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>20.2</td>\n",
       "      <td>272.21</td>\n",
       "      <td>16.23</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>404 rows × 13 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         CRIM     ZN  INDUS  CHAS    NOX     RM   AGE     DIS   RAD    TAX  \\\n",
       "0     5.20177    0.0  18.10   1.0  0.770  6.127  83.4  2.7227  24.0  666.0   \n",
       "1     0.17142    0.0   6.91   0.0  0.448  5.682  33.8  5.1004   3.0  233.0   \n",
       "2     0.09378   12.5   7.87   0.0  0.524  5.889  39.0  5.4509   5.0  311.0   \n",
       "3     0.09252   30.0   4.93   0.0  0.428  6.606  42.2  6.1899   6.0  300.0   \n",
       "4     0.01432  100.0   1.32   0.0  0.411  6.816  40.5  8.3248   5.0  256.0   \n",
       "..        ...    ...    ...   ...    ...    ...   ...     ...   ...    ...   \n",
       "399   0.51183    0.0   6.20   0.0  0.507  7.358  71.6  4.1480   8.0  307.0   \n",
       "400  23.64820    0.0  18.10   0.0  0.671  6.380  96.2  1.3861  24.0  666.0   \n",
       "401   0.04819   80.0   3.64   0.0  0.392  6.108  32.0  9.2203   1.0  315.0   \n",
       "402   1.27346    0.0  19.58   1.0  0.605  6.250  92.6  1.7984   5.0  403.0   \n",
       "403   7.75223    0.0  18.10   0.0  0.713  6.301  83.7  2.7831  24.0  666.0   \n",
       "\n",
       "     PTRATIO       B  LSTAT  \n",
       "0       20.2  395.43  11.48  \n",
       "1       17.9  396.90  10.21  \n",
       "2       15.2  390.50  15.71  \n",
       "3       16.6  383.78   7.37  \n",
       "4       15.1  392.90   3.95  \n",
       "..       ...     ...    ...  \n",
       "399     17.4  390.07   4.73  \n",
       "400     20.2  396.90  23.69  \n",
       "401     16.4  392.89   6.57  \n",
       "402     14.7  338.92   5.50  \n",
       "403     20.2  272.21  16.23  \n",
       "\n",
       "[404 rows x 13 columns]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_boston\n",
    "\n",
    "boston = load_boston()\n",
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "    boston.data, boston.target, test_size=0.2\n",
    ")\n",
    "pd.DataFrame(X_train, columns=boston.feature_names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ".. _boston_dataset:\n",
      "\n",
      "Boston house prices dataset\n",
      "---------------------------\n",
      "\n",
      "**Data Set Characteristics:**  \n",
      "\n",
      "    :Number of Instances: 506 \n",
      "\n",
      "    :Number of Attributes: 13 numeric/categorical predictive. Median Value (attribute 14) is usually the target.\n",
      "\n",
      "    :Attribute Information (in order):\n",
      "        - CRIM     per capita crime rate by town\n",
      "        - ZN       proportion of residential land zoned for lots over 25,000 sq.ft.\n",
      "        - INDUS    proportion of non-retail business acres per town\n",
      "        - CHAS     Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)\n",
      "        - NOX      nitric oxides concentration (parts per 10 million)\n",
      "        - RM       average number of rooms per dwelling\n",
      "        - AGE      proportion of owner-occupied units built prior to 1940\n",
      "        - DIS      weighted distances to five Boston employment centres\n",
      "        - RAD      index of accessibility to radial highways\n",
      "        - TAX      full-value property-tax rate per $10,000\n",
      "        - PTRATIO  pupil-teacher ratio by town\n",
      "        - B        1000(Bk - 0.63)^2 where Bk is the proportion of black people by town\n",
      "        - LSTAT    % lower status of the population\n",
      "        - MEDV     Median value of owner-occupied homes in $1000's\n",
      "\n",
      "    :Missing Attribute Values: None\n",
      "\n",
      "    :Creator: Harrison, D. and Rubinfeld, D.L.\n",
      "\n",
      "This is a copy of UCI ML housing dataset.\n",
      "https://archive.ics.uci.edu/ml/machine-learning-databases/housing/\n",
      "\n",
      "\n",
      "This dataset was taken from the StatLib library which is maintained at Carnegie Mellon University.\n",
      "\n",
      "The Boston house-price data of Harrison, D. and Rubinfeld, D.L. 'Hedonic\n",
      "prices and the demand for clean air', J. Environ. Economics & Management,\n",
      "vol.5, 81-102, 1978.   Used in Belsley, Kuh & Welsch, 'Regression diagnostics\n",
      "...', Wiley, 1980.   N.B. Various transformations are used in the table on\n",
      "pages 244-261 of the latter.\n",
      "\n",
      "The Boston house-price data has been used in many machine learning papers that address regression\n",
      "problems.   \n",
      "     \n",
      ".. topic:: References\n",
      "\n",
      "   - Belsley, Kuh & Welsch, 'Regression diagnostics: Identifying Influential Data and Sources of Collinearity', Wiley, 1980. 244-261.\n",
      "   - Quinlan,R. (1993). Combining Instance-Based and Model-Based Learning. In Proceedings on the Tenth International Conference of Machine Learning, 236-243, University of Massachusetts, Amherst. Morgan Kaufmann.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(boston.DESCR)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### `Ridge` on the Boston housing dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "   fit_time  score_time  test_score  train_score\n",
       "0  0.004382    0.000534    0.743230     0.766721\n",
       "1  0.001129    0.000394    0.787715     0.757490\n",
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       "4  0.001187    0.000509    0.644863     0.788461"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe = make_pipeline(StandardScaler(), Ridge())\n",
    "scores = cross_validate(pipe, X_train, y_train, return_train_score=True)\n",
    "pd.DataFrame(scores)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Hyperparameter `alpha` of `Ridge`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Ridge has hyperparameters just like the rest of the models we learned.\n",
    "- The alpha hyperparameter is what makes `Ridge` different from vanilla `LinearRegression`. \n",
    "- Similar to the other hyperparameters that we saw, `alpha` controls the fundamental tradeoff. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "```{note}\n",
    "If we set alpha=0 that is the same as using LinearRegression.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's examine the effect of `alpha` on the fundamental tradeoff. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "scores_dict = {\n",
    "    \"alpha\": 10.0 ** np.arange(-2, 6, 1),\n",
    "    \"mean_train_scores\": list(),\n",
    "    \"mean_cv_scores\": list(),\n",
    "}\n",
    "for alpha in scores_dict[\"alpha\"]:\n",
    "    pipe_ridge = make_pipeline(StandardScaler(), Ridge(alpha=alpha))\n",
    "    scores = cross_validate(pipe_ridge, X_train, y_train, return_train_score=True)\n",
    "    scores_dict[\"mean_train_scores\"].append(scores[\"train_score\"].mean())\n",
    "    scores_dict[\"mean_cv_scores\"].append(scores[\"test_score\"].mean())\n",
    "\n",
    "results_df = pd.DataFrame(scores_dict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>alpha</th>\n",
       "      <th>mean_train_scores</th>\n",
       "      <th>mean_cv_scores</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.01</td>\n",
       "      <td>0.765604</td>\n",
       "      <td>0.741829</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.10</td>\n",
       "      <td>0.765603</td>\n",
       "      <td>0.741851</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.00</td>\n",
       "      <td>0.765572</td>\n",
       "      <td>0.742040</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>10.00</td>\n",
       "      <td>0.763671</td>\n",
       "      <td>0.741906</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>100.00</td>\n",
       "      <td>0.731996</td>\n",
       "      <td>0.718132</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1000.00</td>\n",
       "      <td>0.527530</td>\n",
       "      <td>0.522510</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>10000.00</td>\n",
       "      <td>0.155124</td>\n",
       "      <td>0.148313</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>100000.00</td>\n",
       "      <td>0.019292</td>\n",
       "      <td>0.010749</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       alpha  mean_train_scores  mean_cv_scores\n",
       "0       0.01           0.765604        0.741829\n",
       "1       0.10           0.765603        0.741851\n",
       "2       1.00           0.765572        0.742040\n",
       "3      10.00           0.763671        0.741906\n",
       "4     100.00           0.731996        0.718132\n",
       "5    1000.00           0.527530        0.522510\n",
       "6   10000.00           0.155124        0.148313\n",
       "7  100000.00           0.019292        0.010749"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "Here we do not really see overfitting but in general, \n",
    "- larger `alpha` $\\rightarrow$ likely to underfit\n",
    "- smaller `alpha` $\\rightarrow$ likely to overfit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Coefficients and intercept\n",
    "\n",
    "The model learns \n",
    "- coefficients associated with each feature\n",
    "- the intercept or bias"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's examine the coefficients learned by the model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "pipe_ridge = make_pipeline(StandardScaler(), Ridge(alpha=1.0))\n",
    "pipe_ridge.fit(X_train, y_train)\n",
    "coeffs = pipe_ridge.named_steps[\"ridge\"].coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Coefficients</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>CRIM</th>\n",
       "      <td>-0.923517</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ZN</th>\n",
       "      <td>1.431294</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>INDUS</th>\n",
       "      <td>0.239976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CHAS</th>\n",
       "      <td>0.546769</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NOX</th>\n",
       "      <td>-2.048052</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RM</th>\n",
       "      <td>2.668174</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AGE</th>\n",
       "      <td>0.035459</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DIS</th>\n",
       "      <td>-3.084434</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RAD</th>\n",
       "      <td>2.407602</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TAX</th>\n",
       "      <td>-2.269648</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PTRATIO</th>\n",
       "      <td>-1.883905</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>0.897462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LSTAT</th>\n",
       "      <td>-3.394533</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Coefficients\n",
       "CRIM        -0.923517\n",
       "ZN           1.431294\n",
       "INDUS        0.239976\n",
       "CHAS         0.546769\n",
       "NOX         -2.048052\n",
       "RM           2.668174\n",
       "AGE          0.035459\n",
       "DIS         -3.084434\n",
       "RAD          2.407602\n",
       "TAX         -2.269648\n",
       "PTRATIO     -1.883905\n",
       "B            0.897462\n",
       "LSTAT       -3.394533"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(data=coeffs, index=boston.feature_names, columns=[\"Coefficients\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- The model also learns an intercept (bias). \n",
    "- For each prediction, we are adding this amount irrespective of the feature values.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "22.446534653465363"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe_ridge.named_steps[\"ridge\"].intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Can we use this information to interpret model predictions? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### ❓❓ Questions for you"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "#### True/False: `Ridge`\n",
    "\n",
    "1. Increasing the hyperparameter `alpha` of `Ridge` is likely to decrease model complexity.\n",
    "2. `Ridge` can be used with datasets that have multiple features.\n",
    "3. With Ridge, we learn one coefficient per training example.\n",
    "4. If you train a linear regression model on a 2-dimensional problem (2 features), the model will be a two dimensional plane. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "<br><br><br><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Interpretation of coefficients "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- One of the main advantages of linear models is that they are relatively easy to interpret. \n",
    "- We have one coefficient per feature which kind of describes the role of the feature in the prediction according to the model. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are two pieces of information in the coefficients based on\n",
    "\n",
    "- Sign\n",
    "- Magnitude"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Sign of the coefficients\n",
    "\n",
    "In the example below, for instance: \n",
    "- RM (average number of rooms) has a **positive coefficient**\n",
    "    - the prediction will be proportional to the feature value; as RM gets **bigger**, the median house value gets **bigger** \n",
    "- CRIM (criminal rate in the neighbourhood) has a **negative coefficient**\n",
    "    - the prediction will be inversely proportional to the feature value; as CRIM gets **bigger**, the median house value gets **smaller**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Coefficients</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>CRIM</th>\n",
       "      <td>-0.923517</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ZN</th>\n",
       "      <td>1.431294</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>INDUS</th>\n",
       "      <td>0.239976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CHAS</th>\n",
       "      <td>0.546769</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NOX</th>\n",
       "      <td>-2.048052</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RM</th>\n",
       "      <td>2.668174</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AGE</th>\n",
       "      <td>0.035459</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DIS</th>\n",
       "      <td>-3.084434</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RAD</th>\n",
       "      <td>2.407602</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TAX</th>\n",
       "      <td>-2.269648</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PTRATIO</th>\n",
       "      <td>-1.883905</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>0.897462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LSTAT</th>\n",
       "      <td>-3.394533</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Coefficients\n",
       "CRIM        -0.923517\n",
       "ZN           1.431294\n",
       "INDUS        0.239976\n",
       "CHAS         0.546769\n",
       "NOX         -2.048052\n",
       "RM           2.668174\n",
       "AGE          0.035459\n",
       "DIS         -3.084434\n",
       "RAD          2.407602\n",
       "TAX         -2.269648\n",
       "PTRATIO     -1.883905\n",
       "B            0.897462\n",
       "LSTAT       -3.394533"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(data=coeffs, index=boston.feature_names, columns=[\"Coefficients\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Magnitude of the coefficients\n",
    "\n",
    "- Bigger magnitude $\\rightarrow$ bigger impact on the prediction \n",
    "- In the example below, both RM and AGE have a positive impact on the prediction but RM would have a bigger positive impact because it's feature value is going to be multiplied by a number with a bigger magnitude. \n",
    "- Similarly both LSAT and NOX have a negative impact on the prediction but LSAT would have a bigger negative impact because it's going to be multiplied by a number with a bigger magnitude. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe thead th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>coefficient</th>\n",
       "      <th>magnitude</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>LSTAT</th>\n",
       "      <td>-3.394533</td>\n",
       "      <td>3.394533</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DIS</th>\n",
       "      <td>-3.084434</td>\n",
       "      <td>3.084434</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RM</th>\n",
       "      <td>2.668174</td>\n",
       "      <td>2.668174</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RAD</th>\n",
       "      <td>2.407602</td>\n",
       "      <td>2.407602</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TAX</th>\n",
       "      <td>-2.269648</td>\n",
       "      <td>2.269648</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NOX</th>\n",
       "      <td>-2.048052</td>\n",
       "      <td>2.048052</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PTRATIO</th>\n",
       "      <td>-1.883905</td>\n",
       "      <td>1.883905</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ZN</th>\n",
       "      <td>1.431294</td>\n",
       "      <td>1.431294</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CRIM</th>\n",
       "      <td>-0.923517</td>\n",
       "      <td>0.923517</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>0.897462</td>\n",
       "      <td>0.897462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CHAS</th>\n",
       "      <td>0.546769</td>\n",
       "      <td>0.546769</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>INDUS</th>\n",
       "      <td>0.239976</td>\n",
       "      <td>0.239976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AGE</th>\n",
       "      <td>0.035459</td>\n",
       "      <td>0.035459</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         coefficient  magnitude\n",
       "LSTAT      -3.394533   3.394533\n",
       "DIS        -3.084434   3.084434\n",
       "RM          2.668174   2.668174\n",
       "RAD         2.407602   2.407602\n",
       "TAX        -2.269648   2.269648\n",
       "NOX        -2.048052   2.048052\n",
       "PTRATIO    -1.883905   1.883905\n",
       "ZN          1.431294   1.431294\n",
       "CRIM       -0.923517   0.923517\n",
       "B           0.897462   0.897462\n",
       "CHAS        0.546769   0.546769\n",
       "INDUS       0.239976   0.239976\n",
       "AGE         0.035459   0.035459"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = {\n",
    "    \"coefficient\": pipe_ridge.named_steps[\"ridge\"].coef_.tolist(),\n",
    "    \"magnitude\": np.absolute(pipe_ridge.named_steps[\"ridge\"].coef_.tolist()),\n",
    "}\n",
    "coef_df = pd.DataFrame(data, index=boston.feature_names).sort_values(\n",
    "    \"magnitude\", ascending=False\n",
    ")\n",
    "coef_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Importance of scaling \n",
    "- When you are interpreting the model coefficients, scaling is crucial. \n",
    "- If you do not scale the data, features with smaller magnitude are going to get coefficients with bigger magnitude whereas features with bigger scale are going to get coefficients with smaller magnitude.\n",
    "- That said, when you scale the data, feature values become hard to interpret for humans!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{Important}\n",
    "Take these coefficients with a grain of salt. They might not always match your intuitions.  \n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### ❓❓ Questions for you"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### True/False\n",
    "\n",
    "1. Suppose you have trained a linear model on an unscaled data. The coefficients of the linear model have the following interpretation: if coefficient $j$ is large, that means a change in feature $j$ has a large impact on the prediction.\n",
    "2. Suppose the scaled feature value of NOX feature above is negative. The prediction will still be inversely proportional to NOX; as NOX gets **bigger**, the median house value gets **smaller**. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Questions for breakout room discussion \n",
    "\n",
    "- Discuss the importance of scaling when interpreting linear regression coefficients. \n",
    "- What might be the meaning of complex vs simpler model in case of linear regression? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br><br><br><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Logistic regression [[video](https://youtu.be/56L5z_t22qE)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### Logistic regression intuition \n",
    "\n",
    "- A linear model for **classification**. \n",
    "- Similar to linear regression, it learns weights associated with each feature and the bias. \n",
    "- It applies a **threshold** on the raw output to decide whether the class is positive or negative. \n",
    "- In this lecture we will focus on the following aspects of logistic regression.  \n",
    "    - `predict`, `predict_proba` \n",
    "    - how to use learned coefficients to interpret the model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Motivating example \n",
    "\n",
    "- Consider the problem of predicting sentiment expressed in movie reviews. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Training data for the motivating example\n",
    "\n",
    "\n",
    "<blockquote> \n",
    "    <p>Review 1: This movie was <b>excellent</b>! The performances were oscar-worthy!  👍 </p> \n",
    "    <p>Review 2: What a <b>boring</b> movie! I almost fell asleep twice while watching it. 👎 </p> \n",
    "    <p>Review 3: I enjoyed the movie. <b>Excellent</b>! 👍 </p>             \n",
    "</blockquote>  \n",
    "\n",
    "- Targets: positive 👍 and negative 👎\n",
    "- Features: words (e.g., *excellent*, *flawless*, *boring*)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Learned coefficients associated with all features\n",
    "\n",
    "- Suppose our vocabulary contains only the following 7 words. \n",
    "- A linear classifier learns **weights** or **coefficients** associated with the features (words in this example).  \n",
    "- Let's ignore bias for a bit. \n",
    "\n",
    "<center>\n",
    "<img src='./img/words_coeff.png' width=\"250\" height=\"300\" />\n",
    "</center>  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Predicting with learned weights \n",
    "- Use these learned coefficients to make predictions. For example, consider the following review $x_i$. \n",
    "<blockquote> \n",
    "It got a bit <b>boring</b> at times but the direction was <b>excellent</b> and the acting was <b>flawless</b>.\n",
    "</blockquote>\n",
    "- Feature vector for $x_i$: [1, 0, 1, 1, 0, 0, 0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<center>\n",
    "<img src='./img/words_coeff.png' width=\"250\" height=\"300\" />\n",
    "</center>  \n",
    "\n",
    "- $score(x_i) = $ coefficient(*boring*) $\\times 1$ + coefficient(*excellent*) $\\times 1$ + coefficient(*flawless*) $\\times 1$ = $-1.40 + 1.93 + 1.43 = 1.96$\n",
    "\n",
    "- $1.96 > 0$ so predict the review as positive 👍. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Weighted sum of the input features = 1.960 y_hat = pos\n"
     ]
    },
    {
     "data": {
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       "</g>\n",
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       "<title>excellent=1</title>\n",
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       "<title>flawless=1</title>\n",
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       "</g>\n",
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       "<text text-anchor=\"middle\" x=\"153.09\" y=\"-140.8\" font-family=\"Times,serif\" font-size=\"14.00\">1.43</text>\n",
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       "<graphviz.dot.Digraph at 0x136483790>"
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     "metadata": {},
     "output_type": "display_data"
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   ],
   "source": [
    "x = [\"boring=1\", \"excellent=1\", \"flawless=1\"]\n",
    "w = [-1.40, 1.93, 1.43]\n",
    "display(plot_logistic_regression(x, w))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- So the prediction is based on the weighted sum of the input features.\n",
    "- Some feature are pulling the prediction towards positive sentiment and some are pulling it towards negative sentiment. \n",
    "- If the coefficient of _boring_ had a bigger magnitude or _excellent_ and _flawless_ had smaller magnitudes, we would have predicted \"neg\".   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def f(w_0):\n",
    "    x = [\"boring=1\", \"excellent=1\", \"flawless=1\"]\n",
    "    w = [-1.40, 1.93, 1.43]\n",
    "    w[0] = w_0\n",
    "    print(w)\n",
    "    display(plot_logistic_regression(x, w))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f585e89458d84b26a94e274dd8af5679",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=-1.4, description='w_0', max=2.0, min=-6.0, step=0.5), Output()), _dom…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "interactive(\n",
    "    f,\n",
    "    w_0=widgets.FloatSlider(min=-6, max=2, step=0.5, value=-1.40),\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "In our case, for values for the coefficient of _boring_ < -3.36, the prediction would be negative. \n",
    "\n",
    "A linear model learns these coefficients or weights from the training data! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "So a linear classifier is a linear function of the input `X`, followed by a threshold. \n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "z =& w_1x_1 + \\dots + w_dx_d + b\\\\\n",
    "=& w^Tx + b\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "\n",
    "$$\\hat{y} = \\begin{cases}\n",
    "         1, & \\text{if } z \\geq r\\\\\n",
    "         -1, & \\text{if } z < r\n",
    "\\end{cases}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Components of a linear classifier\n",
    "\n",
    "1. input features ($x_1, \\dots, x_d$)\n",
    "2. coefficients (weights) ($w_1, \\dots, w_d$)\n",
    "3. bias ($b$ or $w_0$) (can be used to offset your hyperplane)\n",
    "4. threshold ($r$)\n",
    "\n",
    "In our example before, we assumed $r=0$ and $b=0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Logistic regression on the cities data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>longitude</th>\n",
       "      <th>latitude</th>\n",
       "      <th>country</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>160</th>\n",
       "      <td>-76.4813</td>\n",
       "      <td>44.2307</td>\n",
       "      <td>Canada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127</th>\n",
       "      <td>-81.2496</td>\n",
       "      <td>42.9837</td>\n",
       "      <td>Canada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>169</th>\n",
       "      <td>-66.0580</td>\n",
       "      <td>45.2788</td>\n",
       "      <td>Canada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>188</th>\n",
       "      <td>-73.2533</td>\n",
       "      <td>45.3057</td>\n",
       "      <td>Canada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>187</th>\n",
       "      <td>-67.9245</td>\n",
       "      <td>47.1652</td>\n",
       "      <td>Canada</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     longitude  latitude country\n",
       "160   -76.4813   44.2307  Canada\n",
       "127   -81.2496   42.9837  Canada\n",
       "169   -66.0580   45.2788  Canada\n",
       "188   -73.2533   45.3057  Canada\n",
       "187   -67.9245   47.1652  Canada"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cities_df = pd.read_csv(\"data/canada_usa_cities.csv\")\n",
    "train_df, test_df = train_test_split(cities_df, test_size=0.2, random_state=123)\n",
    "X_train, y_train = train_df.drop(columns=[\"country\"], axis=1), train_df[\"country\"]\n",
    "X_test, y_test = test_df.drop(columns=[\"country\"], axis=1), test_df[\"country\"]\n",
    "\n",
    "train_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's first try `DummyClassifier` on the cities data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>fit_time</th>\n",
       "      <th>score_time</th>\n",
       "      <th>test_score</th>\n",
       "      <th>train_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.000587</td>\n",
       "      <td>0.000456</td>\n",
       "      <td>0.588235</td>\n",
       "      <td>0.601504</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.000638</td>\n",
       "      <td>0.000273</td>\n",
       "      <td>0.588235</td>\n",
       "      <td>0.601504</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.000441</td>\n",
       "      <td>0.000263</td>\n",
       "      <td>0.606061</td>\n",
       "      <td>0.597015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.000427</td>\n",
       "      <td>0.000275</td>\n",
       "      <td>0.606061</td>\n",
       "      <td>0.597015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.000481</td>\n",
       "      <td>0.000260</td>\n",
       "      <td>0.606061</td>\n",
       "      <td>0.597015</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   fit_time  score_time  test_score  train_score\n",
       "0  0.000587    0.000456    0.588235     0.601504\n",
       "1  0.000638    0.000273    0.588235     0.601504\n",
       "2  0.000441    0.000263    0.606061     0.597015\n",
       "3  0.000427    0.000275    0.606061     0.597015\n",
       "4  0.000481    0.000260    0.606061     0.597015"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dummy = DummyClassifier()\n",
    "scores = cross_validate(dummy, X_train, y_train, return_train_score=True)\n",
    "pd.DataFrame(scores)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Now let's try `LogisticRegression`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>fit_time</th>\n",
       "      <th>score_time</th>\n",
       "      <th>test_score</th>\n",
       "      <th>train_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.008575</td>\n",
       "      <td>0.001083</td>\n",
       "      <td>0.852941</td>\n",
       "      <td>0.827068</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.007072</td>\n",
       "      <td>0.001045</td>\n",
       "      <td>0.823529</td>\n",
       "      <td>0.827068</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.005295</td>\n",
       "      <td>0.001079</td>\n",
       "      <td>0.696970</td>\n",
       "      <td>0.858209</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.005661</td>\n",
       "      <td>0.000888</td>\n",
       "      <td>0.787879</td>\n",
       "      <td>0.843284</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.005895</td>\n",
       "      <td>0.001320</td>\n",
       "      <td>0.939394</td>\n",
       "      <td>0.805970</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   fit_time  score_time  test_score  train_score\n",
       "0  0.008575    0.001083    0.852941     0.827068\n",
       "1  0.007072    0.001045    0.823529     0.827068\n",
       "2  0.005295    0.001079    0.696970     0.858209\n",
       "3  0.005661    0.000888    0.787879     0.843284\n",
       "4  0.005895    0.001320    0.939394     0.805970"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "lr = LogisticRegression()\n",
    "scores = cross_validate(lr, X_train, y_train, return_train_score=True)\n",
    "pd.DataFrame(scores)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Logistic regression seems to be doing better than dummy classifier. But note that there is a lot of variation in the scores. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Accessing learned parameters\n",
    "\n",
    "- Recall that logistic regression learns the weights $w$ and bias or intercept $b$.\n",
    "\n",
    "- How to access these weights? \n",
    "    - Similar to `Ridge`, we can access the weights and intercept using `coef_` and `intercept_` attribute of the `LogisticRegression` object, respectively. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model weights: [[-0.04108149 -0.33683126]]\n",
      "Model intercept: [10.8869838]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>features</th>\n",
       "      <th>coefficients</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>longitude</td>\n",
       "      <td>-0.041081</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>latitude</td>\n",
       "      <td>-0.336831</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    features  coefficients\n",
       "0  longitude     -0.041081\n",
       "1   latitude     -0.336831"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr = LogisticRegression()\n",
    "lr.fit(X_train, y_train)\n",
    "print(\"Model weights: %s\" % (lr.coef_))  # these are the learned weights\n",
    "print(\"Model intercept: %s\" % (lr.intercept_))  # this is the bias term\n",
    "data = {\"features\": X_train.columns, \"coefficients\": lr.coef_[0]}\n",
    "pd.DataFrame(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Both negative weights \n",
    "- The weight of latitude is larger in magnitude. \n",
    "- This makes sense because Canada as a country lies above the USA and so we expect latitude values to contribute more to a prediction than longitude. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Prediction with learned parameters\n",
    "\n",
    "Let's predict target of a test example. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "longitude   -64.8001\n",
       "latitude     46.0980\n",
       "Name: 172, dtype: float64"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "example = X_test.iloc[0, :]\n",
    "example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Raw scores\n",
    "\n",
    "- Calculate the raw score as: ```y_hat = np.dot(w, x) + b```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.97817876])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(\n",
    "    np.dot(\n",
    "        example.to_numpy(),\n",
    "        lr.coef_.reshape(\n",
    "            2,\n",
    "        ),\n",
    "    )\n",
    "    + lr.intercept_\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Apply the threshold to the raw score. \n",
    "- Since the prediction is < 0, predict \"negative\". \n",
    "- What is a \"negative\" class in our context? \n",
    "- With logistic regression, the model randomly assigns one of the classes as a positive class and the other as negative. \n",
    "    - Usually it would alphabetically order the target and pick the first one as negative and second one as the positive class. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- The `classes_` attribute tells us which class is considered negative and which one is considered positive. - In this case, Canada is the negative class and USA is a positive class. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Canada', 'USA'], dtype=object)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.classes_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- So based on the negative score above (-1.978), we would predict Canada. \n",
    "- Let's check the prediction given by the model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/kvarada/opt/miniconda3/envs/571/lib/python3.9/site-packages/sklearn/base.py:441: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array(['Canada'], dtype=object)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.predict([example])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Great! The predictions match! We exactly know how the model is making predictions. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Decision boundary of logistic regression\n",
    "\n",
    "- The decision boundary of logistic regression is a **hyperplane** dividing the feature space in half. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/kvarada/opt/miniconda3/envs/571/lib/python3.9/site-packages/sklearn/base.py:441: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lr = LogisticRegression()\n",
    "lr.fit(X_train, y_train)\n",
    "mglearn.discrete_scatter(X_train.iloc[:, 0], X_train.iloc[:, 1], y_train)\n",
    "mglearn.plots.plot_2d_separator(lr, X_train.to_numpy(), fill=False, eps=0.5, alpha=0.7)\n",
    "plt.title(lr.__class__.__name__)\n",
    "plt.xlabel(\"longitude\")\n",
    "plt.ylabel(\"latitude\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- For $d=2$, the decision boundary is a line (1-dimensional)\n",
    "- For $d=3$, the decision boundary is a plane (2-dimensional)\n",
    "- For $d\\gt 3$, the decision boundary is a $d-1$-dimensional hyperplane"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/kvarada/opt/miniconda3/envs/571/lib/python3.9/site-packages/sklearn/base.py:441: UserWarning: X does not have valid feature names, but KNeighborsClassifier was fitted with feature names\n",
      "  warnings.warn(\n",
      "/Users/kvarada/opt/miniconda3/envs/571/lib/python3.9/site-packages/sklearn/base.py:441: UserWarning: X does not have valid feature names, but KNeighborsClassifier was fitted with feature names\n",
      "  warnings.warn(\n",
      "/Users/kvarada/opt/miniconda3/envs/571/lib/python3.9/site-packages/sklearn/base.py:441: UserWarning: X does not have valid feature names, but SVC was fitted with feature names\n",
      "  warnings.warn(\n",
      "/Users/kvarada/opt/miniconda3/envs/571/lib/python3.9/site-packages/sklearn/base.py:441: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x360 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 3, figsize=(20, 5))\n",
    "for model, ax in zip(\n",
    "    [KNeighborsClassifier(), SVC(gamma=0.01), LogisticRegression()], axes\n",
    "):\n",
    "    clf = model.fit(X_train, y_train)\n",
    "    mglearn.plots.plot_2d_separator(\n",
    "        clf, X_train.to_numpy(), fill=True, eps=0.5, ax=ax, alpha=0.4\n",
    "    )\n",
    "    mglearn.discrete_scatter(X_train.iloc[:, 0], X_train.iloc[:, 1], y_train, ax=ax)\n",
    "    ax.set_title(clf.__class__.__name__)\n",
    "    ax.set_xlabel(\"longitude\")\n",
    "    ax.set_ylabel(\"latitude\")\n",
    "axes[0].legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Notice a linear decision boundary (a line in our case). \n",
    "- Compare it with  KNN or SVM RBF decision boundaries. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Main hyperparameter of logistic regression \n",
    "\n",
    "- `C` is the main hyperparameter which controls the fundamental trade-off.\n",
    "- We won't really talk about the interpretation of this hyperparameter right now. \n",
    "- At a high level, the interpretation is similar to `C` of SVM RBF\n",
    "    - smaller `C` $\\rightarrow$ might lead to underfitting\n",
    "    - bigger `C` $\\rightarrow$ might lead to overfitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>C</th>\n",
       "      <th>mean_train_scores</th>\n",
       "      <th>mean_cv_scores</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0001</td>\n",
       "      <td>0.664707</td>\n",
       "      <td>0.658645</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0010</td>\n",
       "      <td>0.784424</td>\n",
       "      <td>0.790731</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.0100</td>\n",
       "      <td>0.827842</td>\n",
       "      <td>0.826203</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.1000</td>\n",
       "      <td>0.832320</td>\n",
       "      <td>0.820143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0000</td>\n",
       "      <td>0.832320</td>\n",
       "      <td>0.820143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>10.0000</td>\n",
       "      <td>0.832320</td>\n",
       "      <td>0.820143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>100.0000</td>\n",
       "      <td>0.832320</td>\n",
       "      <td>0.820143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1000.0000</td>\n",
       "      <td>0.832320</td>\n",
       "      <td>0.820143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>10000.0000</td>\n",
       "      <td>0.832320</td>\n",
       "      <td>0.820143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>100000.0000</td>\n",
       "      <td>0.832320</td>\n",
       "      <td>0.820143</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             C  mean_train_scores  mean_cv_scores\n",
       "0       0.0001           0.664707        0.658645\n",
       "1       0.0010           0.784424        0.790731\n",
       "2       0.0100           0.827842        0.826203\n",
       "3       0.1000           0.832320        0.820143\n",
       "4       1.0000           0.832320        0.820143\n",
       "5      10.0000           0.832320        0.820143\n",
       "6     100.0000           0.832320        0.820143\n",
       "7    1000.0000           0.832320        0.820143\n",
       "8   10000.0000           0.832320        0.820143\n",
       "9  100000.0000           0.832320        0.820143"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scores_dict = {\n",
    "    \"C\": 10.0 ** np.arange(-4, 6, 1),\n",
    "    \"mean_train_scores\": list(),\n",
    "    \"mean_cv_scores\": list(),\n",
    "}\n",
    "for C in scores_dict[\"C\"]:\n",
    "    lr = LogisticRegression(C=C)\n",
    "    scores = cross_validate(lr, X_train, y_train, return_train_score=True)\n",
    "    scores_dict[\"mean_train_scores\"].append(scores[\"train_score\"].mean())\n",
    "    scores_dict[\"mean_cv_scores\"].append(scores[\"test_score\"].mean())\n",
    "\n",
    "results_df = pd.DataFrame(scores_dict)\n",
    "results_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br><br><br><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Predicting probability scores [[video](https://youtu.be/_OAK5KiGLg0)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### `predict_proba`\n",
    "\n",
    "- So far in the context of classification problems, we focused on getting \"hard\" predictions. \n",
    "- Very often it's useful to know \"soft\" predictions, i.e., how confident the model is with a given prediction.  \n",
    "- For most of the `scikit-learn` classification models we can access this confidence score or probability score using a method called `predict_proba`.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's look at probability scores of logistic regression model for our test example. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "longitude   -64.8001\n",
       "latitude     46.0980\n",
       "Name: 172, dtype: float64"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/kvarada/opt/miniconda3/envs/571/lib/python3.9/site-packages/sklearn/base.py:441: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array(['Canada'], dtype=object)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr = LogisticRegression()\n",
    "lr.fit(X_train, y_train)\n",
    "lr.predict([example])  # hard prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/kvarada/opt/miniconda3/envs/571/lib/python3.9/site-packages/sklearn/base.py:441: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[0.87848688, 0.12151312]])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.predict_proba([example])  # soft prediction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- The output of `predict_proba` is the probability of each class. \n",
    "- In binary classification, we get probabilities associated with both classes (even though this information is redundant). \n",
    "- The first entry is the estimated probability of the first class and the second entry is the estimated probability of the second class from `model.classes_`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Canada', 'USA'], dtype=object)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.classes_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Because it's a probability, the sum of the entries for both classes should always sum to 1. \n",
    "- Since the probabilities for the two classes sum to 1, exactly one of the classes will have a score >=0.5, which is going to be our predicted class.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### How does logistic regression calculate these probabilities? \n",
    "\n",
    "- The weighted sum $w_1x_1 + \\dots + w_dx_d + b$ gives us \"raw model output\".\n",
    "- For linear regression this would have been the prediction.\n",
    "- For logistic regression, you check the **sign** of this value.\n",
    "  - If positive (or 0), predict $+1$; if negative, predict $-1$.\n",
    "  - These are \"hard predictions\"."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- You can also have \"soft predictions\", aka **predicted probabilities**. \n",
    "  - To convert the raw model output into probabilities, instead of taking the sign, we apply the **sigmoid**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### The sigmoid function \n",
    "- The sigmoid function \"squashes\" the raw model output from any number to the range $[0,1]$ using the following formula, where $x$ is the raw model output. \n",
    "$$\\frac{1}{1+e^{-x}}$$\n",
    "- Then we can interpret the output as probabilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sigmoid = lambda x: 1 / (1 + np.exp(-x))\n",
    "raw_model_output = np.linspace(-8, 8, 1000)\n",
    "plt.plot(raw_model_output, sigmoid(raw_model_output))\n",
    "plt.plot([0, 0], [0, 0.5], \"--k\")\n",
    "plt.plot([-8, 0], [0.5, 0.5], \"--k\")\n",
    "plt.xlabel(\"raw model output, $w^Tx$\")\n",
    "plt.ylabel(\"predicted probability\")\n",
    "plt.title(\"the sigmoid function\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Recall our hard predictions that check the sign of $w^Tx$, or, in other words, whether or not it is $\\geq 0$.\n",
    "  - The threshold $w^Tx=0$ corresponds to $p=0.5$. \n",
    "  - In other words, if our predicted probability is $\\geq 0.5$ then our hard prediction is $+1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's get the probability score by calling sigmoid on the raw model output for our test example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.12151312])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sigmoid(\n",
    "    np.dot(\n",
    "        example.to_numpy(),\n",
    "        lr.coef_.reshape(\n",
    "            2,\n",
    "        ),\n",
    "    )\n",
    "    + lr.intercept_\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the probability score of the positive class, which is USA. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/kvarada/opt/miniconda3/envs/571/lib/python3.9/site-packages/sklearn/base.py:441: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[0.87848688, 0.12151312]])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.predict_proba([example])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With `predict_proba`, we get the same probability score for USA!!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Let's visualize probability scores for some examples. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "data_dict = {\n",
    "    \"y\": y_train[:12],\n",
    "    \"y_hat\": lr.predict(X_train[:12]).tolist(),\n",
    "    \"probabilities\": lr.predict_proba(X_train[:12]).tolist(),\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>y_hat</th>\n",
       "      <th>probabilities</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>160</th>\n",
       "      <td>Canada</td>\n",
       "      <td>Canada</td>\n",
       "      <td>[0.7046068097086481, 0.2953931902913519]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127</th>\n",
       "      <td>Canada</td>\n",
       "      <td>Canada</td>\n",
       "      <td>[0.5630169062040135, 0.43698309379598654]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>169</th>\n",
       "      <td>Canada</td>\n",
       "      <td>Canada</td>\n",
       "      <td>[0.8389680973255864, 0.16103190267441364]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>188</th>\n",
       "      <td>Canada</td>\n",
       "      <td>Canada</td>\n",
       "      <td>[0.7964150775404333, 0.20358492245956678]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>187</th>\n",
       "      <td>Canada</td>\n",
       "      <td>Canada</td>\n",
       "      <td>[0.9010806652340972, 0.0989193347659027]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>192</th>\n",
       "      <td>Canada</td>\n",
       "      <td>Canada</td>\n",
       "      <td>[0.7753006388010791, 0.2246993611989209]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>62</th>\n",
       "      <td>USA</td>\n",
       "      <td>USA</td>\n",
       "      <td>[0.030740704606528002, 0.969259295393472]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>141</th>\n",
       "      <td>Canada</td>\n",
       "      <td>Canada</td>\n",
       "      <td>[0.6880304799160921, 0.3119695200839079]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>183</th>\n",
       "      <td>Canada</td>\n",
       "      <td>Canada</td>\n",
       "      <td>[0.7891358587234145, 0.21086414127658554]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>USA</td>\n",
       "      <td>USA</td>\n",
       "      <td>[0.006546969753885579, 0.9934530302461144]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>USA</td>\n",
       "      <td>USA</td>\n",
       "      <td>[0.27874195848431016, 0.7212580415156898]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>89</th>\n",
       "      <td>Canada</td>\n",
       "      <td>Canada</td>\n",
       "      <td>[0.838887714664494, 0.16111228533550606]</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          y   y_hat                               probabilities\n",
       "160  Canada  Canada    [0.7046068097086481, 0.2953931902913519]\n",
       "127  Canada  Canada   [0.5630169062040135, 0.43698309379598654]\n",
       "169  Canada  Canada   [0.8389680973255864, 0.16103190267441364]\n",
       "188  Canada  Canada   [0.7964150775404333, 0.20358492245956678]\n",
       "187  Canada  Canada    [0.9010806652340972, 0.0989193347659027]\n",
       "192  Canada  Canada    [0.7753006388010791, 0.2246993611989209]\n",
       "62      USA     USA   [0.030740704606528002, 0.969259295393472]\n",
       "141  Canada  Canada    [0.6880304799160921, 0.3119695200839079]\n",
       "183  Canada  Canada   [0.7891358587234145, 0.21086414127658554]\n",
       "37      USA     USA  [0.006546969753885579, 0.9934530302461144]\n",
       "50      USA     USA   [0.27874195848431016, 0.7212580415156898]\n",
       "89   Canada  Canada    [0.838887714664494, 0.16111228533550606]"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(data_dict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "The actual `y` and `y_hat` match in most of the cases but in some cases the model is more confident about the prediction than others. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Least confident cases \n",
    "\n",
    "Let's examine some cases where the model is least confident about the prediction. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>longitude</th>\n",
       "      <th>latitude</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>127</th>\n",
       "      <td>-81.2496</td>\n",
       "      <td>42.9837</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>141</th>\n",
       "      <td>-79.6902</td>\n",
       "      <td>44.3893</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     longitude  latitude\n",
       "127   -81.2496   42.9837\n",
       "141   -79.6902   44.3893"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "least_confident_X = X_train.loc[[127, 141]]\n",
    "least_confident_X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "127    Canada\n",
       "141    Canada\n",
       "Name: country, dtype: object"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "least_confident_y = y_train.loc[[127, 141]]\n",
    "least_confident_y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>y_hat</th>\n",
       "      <th>probability score (Canada)</th>\n",
       "      <th>probability score (USA)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>127</th>\n",
       "      <td>Canada</td>\n",
       "      <td>Canada</td>\n",
       "      <td>0.563017</td>\n",
       "      <td>0.436983</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>141</th>\n",
       "      <td>Canada</td>\n",
       "      <td>Canada</td>\n",
       "      <td>0.688030</td>\n",
       "      <td>0.311970</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          y   y_hat  probability score (Canada)  probability score (USA)\n",
       "127  Canada  Canada                    0.563017                 0.436983\n",
       "141  Canada  Canada                    0.688030                 0.311970"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "probs = lr.predict_proba(least_confident_X)\n",
    "\n",
    "data_dict = {\n",
    "    \"y\": least_confident_y,\n",
    "    \"y_hat\": lr.predict(least_confident_X).tolist(),\n",
    "    \"probability score (Canada)\": probs[:, 0],\n",
    "    \"probability score (USA)\": probs[:, 1],\n",
    "}\n",
    "pd.DataFrame(data_dict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/kvarada/opt/miniconda3/envs/571/lib/python3.9/site-packages/sklearn/base.py:441: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mglearn.discrete_scatter(\n",
    "    least_confident_X.iloc[:, 0],\n",
    "    least_confident_X.iloc[:, 1],\n",
    "    least_confident_y,\n",
    "    markers=\"o\",\n",
    ")\n",
    "mglearn.plots.plot_2d_separator(lr, X_train.to_numpy(), fill=True, eps=0.5, alpha=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The points are close to the decision boundary which makes sense. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Most confident cases \n",
    "\n",
    "Let's examine some cases where the model is most confident about the prediction. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>longitude</th>\n",
       "      <th>latitude</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>-98.4951</td>\n",
       "      <td>29.4246</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>165</th>\n",
       "      <td>-52.7151</td>\n",
       "      <td>47.5617</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     longitude  latitude\n",
       "37    -98.4951   29.4246\n",
       "165   -52.7151   47.5617"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "most_confident_X = X_train.loc[[37, 165]]\n",
    "most_confident_X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "37        USA\n",
       "165    Canada\n",
       "Name: country, dtype: object"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "most_confident_y = y_train.loc[[37, 165]]\n",
    "most_confident_y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>y_hat</th>\n",
       "      <th>probability score (Canada)</th>\n",
       "      <th>probability score (USA)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>USA</td>\n",
       "      <td>USA</td>\n",
       "      <td>0.006547</td>\n",
       "      <td>0.993453</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>165</th>\n",
       "      <td>Canada</td>\n",
       "      <td>Canada</td>\n",
       "      <td>0.951092</td>\n",
       "      <td>0.048908</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          y   y_hat  probability score (Canada)  probability score (USA)\n",
       "37      USA     USA                    0.006547                 0.993453\n",
       "165  Canada  Canada                    0.951092                 0.048908"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "probs = lr.predict_proba(most_confident_X)\n",
    "\n",
    "data_dict = {\n",
    "    \"y\": most_confident_y,\n",
    "    \"y_hat\": lr.predict(most_confident_X).tolist(),\n",
    "    \"probability score (Canada)\": probs[:, 0],\n",
    "    \"probability score (USA)\": probs[:, 1],\n",
    "}\n",
    "pd.DataFrame(data_dict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>longitude</th>\n",
       "      <th>latitude</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>-98.4951</td>\n",
       "      <td>29.4246</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>165</th>\n",
       "      <td>-52.7151</td>\n",
       "      <td>47.5617</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     longitude  latitude\n",
       "37    -98.4951   29.4246\n",
       "165   -52.7151   47.5617"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "most_confident_X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/kvarada/opt/miniconda3/envs/571/lib/python3.9/site-packages/sklearn/base.py:441: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mglearn.discrete_scatter(\n",
    "    most_confident_X.iloc[:, 0],\n",
    "    most_confident_X.iloc[:, 1],\n",
    "    most_confident_y,\n",
    "    markers=\"o\",\n",
    ")\n",
    "mglearn.plots.plot_2d_separator(lr, X_train.to_numpy(), fill=True, eps=0.5, alpha=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The points are far away from the decision boundary which makes sense. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Over confident cases\n",
    "\n",
    "Let's examine some cases where the model is confident about the prediction but the prediction is wrong. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>longitude</th>\n",
       "      <th>latitude</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-130.0437</td>\n",
       "      <td>55.9773</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-134.4197</td>\n",
       "      <td>58.3019</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   longitude  latitude\n",
       "0  -130.0437   55.9773\n",
       "1  -134.4197   58.3019"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "over_confident_X = X_train.loc[[0, 1]]\n",
    "over_confident_X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    USA\n",
       "1    USA\n",
       "Name: country, dtype: object"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "over_confident_y = y_train.loc[[0, 1]]\n",
    "over_confident_y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>y_hat</th>\n",
       "      <th>probability score (Canada)</th>\n",
       "      <th>probability score (USA)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>USA</td>\n",
       "      <td>Canada</td>\n",
       "      <td>0.932487</td>\n",
       "      <td>0.067513</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>USA</td>\n",
       "      <td>Canada</td>\n",
       "      <td>0.961902</td>\n",
       "      <td>0.038098</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     y   y_hat  probability score (Canada)  probability score (USA)\n",
       "0  USA  Canada                    0.932487                 0.067513\n",
       "1  USA  Canada                    0.961902                 0.038098"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "probs = lr.predict_proba(over_confident_X)\n",
    "\n",
    "data_dict = {\n",
    "    \"y\": over_confident_y,\n",
    "    \"y_hat\": lr.predict(over_confident_X).tolist(),\n",
    "    \"probability score (Canada)\": probs[:, 0],\n",
    "    \"probability score (USA)\": probs[:, 1],\n",
    "}\n",
    "pd.DataFrame(data_dict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/kvarada/opt/miniconda3/envs/571/lib/python3.9/site-packages/sklearn/base.py:441: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mglearn.discrete_scatter(\n",
    "    over_confident_X.iloc[:, 0],\n",
    "    over_confident_X.iloc[:, 1],\n",
    "    over_confident_y,\n",
    "    markers=\"o\",\n",
    ")\n",
    "mglearn.plots.plot_2d_separator(lr, X_train.to_numpy(), fill=True, eps=0.5, alpha=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The cities are far away from the decision boundary. So the model is pretty confident about the prediction. \n",
    "- But the cities are likely to be from Alaska and our linear model is not able to capture that this part belong to the USA and not Canada."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Below we are using colour to represent prediction probabilities. If you are closer to the border, the model is less confident whereas the model is more confident about the mainland cities, which makes sense.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/kvarada/opt/miniconda3/envs/571/lib/python3.9/site-packages/sklearn/base.py:441: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n",
      "  warnings.warn(\n",
      "/Users/kvarada/opt/miniconda3/envs/571/lib/python3.9/site-packages/sklearn/base.py:441: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n",
      "  warnings.warn(\n",
      "/Users/kvarada/opt/miniconda3/envs/571/lib/python3.9/site-packages/sklearn/base.py:441: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(18, 5))\n",
    "from matplotlib.colors import ListedColormap\n",
    "\n",
    "for ax in axes:\n",
    "    mglearn.discrete_scatter(\n",
    "        X_train.iloc[:, 0], X_train.iloc[:, 1], y_train, markers=\"o\", ax=ax\n",
    "    )\n",
    "    ax.set_xlabel(\"longitude\")\n",
    "    ax.set_ylabel(\"latitude\")\n",
    "\n",
    "axes[0].legend([\"Train class 0\", \"Train class 1\"], ncol=2, loc=(0.1, 1.1))\n",
    "\n",
    "mglearn.plots.plot_2d_separator(\n",
    "    lr, X_train.to_numpy(), fill=True, eps=0.5, ax=axes[0], alpha=0.5\n",
    ")\n",
    "mglearn.plots.plot_2d_separator(\n",
    "    lr, X_train.to_numpy(), fill=False, eps=0.5, ax=axes[1], alpha=0.5\n",
    ")\n",
    "scores_image = mglearn.tools.plot_2d_scores(\n",
    "    lr, X_train.to_numpy(), eps=0.5, ax=axes[1], alpha=0.5, cm=plt.cm.coolwarm\n",
    ")\n",
    "cbar = plt.colorbar(scores_image, ax=axes.tolist())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Sometimes a complex model that is overfitted, tends to make more confident predictions, even if they are wrong, whereas a simpler model tends to make predictions with more uncertainty. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "To summarize, \n",
    "- With hard predictions, we only know the class. \n",
    "- With probability scores we know how confident the model is with certain predictions, which can be useful in understanding the model better. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### ❓❓ Questions for you"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### True/False\n",
    "\n",
    "- Increasing logistic regression's `C` hyperparameter increases model complexity.\n",
    "- Unlike with `Ridge` regression, coefficients are not interpretable with logistic regression.\n",
    "- The raw output score can be used to calculate the probability score for a given prediction. \n",
    "- For linear classifier trained on $d$ features, the decision boundary is a $d-1$-dimensional hyperparlane.  \n",
    "- A linear model is likely to be uncertain about the data points close to the decision boundary. \n",
    "- Similar to decision trees, conceptually logistic regression should be able to work with categorical features.\n",
    "- Scaling might be a good idea in the context of logistic regression. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Linear SVM \n",
    "\n",
    "- We have seen non-linear SVM with RBF kernel before. This is the default SVC model in `sklearn` because it tends to work better in many cases. \n",
    "- There is also a linear SVM. You can pass `kernel=\"linear\"` to create a linear SVM. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "cities_df = pd.read_csv(\"data/canada_usa_cities.csv\")\n",
    "train_df, test_df = train_test_split(cities_df, test_size=0.2, random_state=123)\n",
    "X_train, y_train = train_df.drop(columns=[\"country\"], axis=1), train_df[\"country\"]\n",
    "X_test, y_test = test_df.drop(columns=[\"country\"], axis=1), test_df[\"country\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/kvarada/opt/miniconda3/envs/571/lib/python3.9/site-packages/sklearn/base.py:441: UserWarning: X does not have valid feature names, but SVC was fitted with feature names\n",
      "  warnings.warn(\n",
      "/Users/kvarada/opt/miniconda3/envs/571/lib/python3.9/site-packages/sklearn/base.py:441: UserWarning: X does not have valid feature names, but SVC was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(18, 5))\n",
    "from matplotlib.colors import ListedColormap\n",
    "\n",
    "for (model, ax) in zip([SVC(gamma=0.01), SVC(kernel=\"linear\")], axes):\n",
    "    mglearn.discrete_scatter(\n",
    "        X_train.iloc[:, 0], X_train.iloc[:, 1], y_train, markers=\"o\", ax=ax\n",
    "    )\n",
    "    model.fit(X_train, y_train)\n",
    "    ax.set_xlabel(\"longitude\")\n",
    "    ax.set_ylabel(\"latitude\")\n",
    "    mglearn.plots.plot_2d_separator(\n",
    "        model, X_train.to_numpy(), fill=True, eps=0.5, ax=ax, alpha=0.5\n",
    "    )\n",
    "\n",
    "axes[0].set_title(\"SVM RBF\")\n",
    "axes[1].set_title(\"Linear SVM\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- `predict` method of linear SVM and logistic regression works the same way. \n",
    "- We can get `coef_` associated with the features and `intercept_` using a Linear SVM model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model weights: [[-0.0195598  -0.23640124]]\n",
      "Model intercept: [8.22811601]\n"
     ]
    }
   ],
   "source": [
    "linear_svc = SVC(kernel=\"linear\")\n",
    "linear_svc.fit(X_train, y_train)\n",
    "print(\"Model weights: %s\" % (linear_svc.coef_))\n",
    "print(\"Model intercept: %s\" % (linear_svc.intercept_))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model weights: [[-0.04108149 -0.33683126]]\n",
      "Model intercept: [10.8869838]\n"
     ]
    }
   ],
   "source": [
    "lr = LogisticRegression()\n",
    "lr.fit(X_train, y_train)\n",
    "print(\"Model weights: %s\" % (lr.coef_))\n",
    "print(\"Model intercept: %s\" % (lr.intercept_))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Note that the coefficients and intercept are slightly different for logistic regression. \n",
    "- This is because the `fit` for linear SVM and logistic regression are different. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br><br><br><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Model interpretation of linear classifiers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- One of the primary advantage of linear classifiers is their ability to interpret models. \n",
    "- For example, with the sign and magnitude of learned coefficients we could answer questions such as which features are driving the prediction to which direction. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- We'll demonstrate this by training `LogisticRegression` on the famous [IMDB movie review](https://www.kaggle.com/lakshmi25npathi/imdb-dataset-of-50k-movie-reviews) dataset. The dataset is a bit large for demonstration purposes. So I am going to put a big portion of it in the test split to speed things up. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>review</th>\n",
       "      <th>label</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Once again Mr. Costner has dragged out a movie for far longer than necessary. Aside from the terrific sea rescue sequences, of which there are very few I just did not care about any of the charact...</td>\n",
       "      <td>neg</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>This is an example of why the majority of action films are the same. Generic and boring, there's really nothing worth watching here. A complete waste of the then barely-tapped talents of Ice-T and...</td>\n",
       "      <td>neg</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>First of all I hate those moronic rappers, who could'nt act if they had a gun pressed against their foreheads. All they do is curse and shoot each other and acting like clichÃ©'e version of gangst...</td>\n",
       "      <td>neg</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Not even the Beatles could write songs everyone liked, and although Walter Hill is no mop-top he's second to none when it comes to thought provoking action movies. The nineties came and social pla...</td>\n",
       "      <td>neg</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Brass pictures (movies is not a fitting word for them) really are somewhat brassy. Their alluring visual qualities are reminiscent of expensive high class TV commercials. But unfortunately Brass p...</td>\n",
       "      <td>neg</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                                                                                                                                                                    review  \\\n",
       "0  Once again Mr. Costner has dragged out a movie for far longer than necessary. Aside from the terrific sea rescue sequences, of which there are very few I just did not care about any of the charact...   \n",
       "1  This is an example of why the majority of action films are the same. Generic and boring, there's really nothing worth watching here. A complete waste of the then barely-tapped talents of Ice-T and...   \n",
       "2  First of all I hate those moronic rappers, who could'nt act if they had a gun pressed against their foreheads. All they do is curse and shoot each other and acting like clichÃ©'e version of gangst...   \n",
       "3  Not even the Beatles could write songs everyone liked, and although Walter Hill is no mop-top he's second to none when it comes to thought provoking action movies. The nineties came and social pla...   \n",
       "4  Brass pictures (movies is not a fitting word for them) really are somewhat brassy. Their alluring visual qualities are reminiscent of expensive high class TV commercials. But unfortunately Brass p...   \n",
       "\n",
       "  label  \n",
       "0   neg  \n",
       "1   neg  \n",
       "2   neg  \n",
       "3   neg  \n",
       "4   neg  "
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "imdb_df = pd.read_csv(\"data/imdb_master.csv\", encoding=\"ISO-8859-1\")\n",
    "imdb_df = imdb_df[imdb_df[\"label\"].str.startswith((\"pos\", \"neg\"))]\n",
    "imdb_df.drop([\"Unnamed: 0\", \"type\", \"file\"], axis=1, inplace=True)\n",
    "imdb_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's clean up the data a bit. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "import re\n",
    "\n",
    "\n",
    "def replace_tags(doc):\n",
    "    doc = doc.replace(\"<br />\", \" \")\n",
    "    doc = re.sub(\"https://\\S*\", \"\", doc)\n",
    "    return doc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "imdb_df[\"review_pp\"] = imdb_df[\"review\"].apply(replace_tags)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Are we breaking the Golden rule here? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's split the data and create bag of words representation. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5000, 3)"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_df, test_df = train_test_split(imdb_df, test_size=0.9, random_state=123)\n",
    "X_train, y_train = train_df[\"review_pp\"], train_df[\"label\"]\n",
    "X_test, y_test = test_df[\"review_pp\"], test_df[\"label\"]\n",
    "train_df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<5000x10000 sparse matrix of type '<class 'numpy.int64'>'\n",
       "\twith 383702 stored elements in Compressed Sparse Row format>"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vec = CountVectorizer(stop_words=\"english\", max_features=10000)\n",
    "bow = vec.fit_transform(X_train)\n",
    "bow"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Examining the vocabulary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- The vocabulary (mapping from feature indices to actual words) can be obtained using `get_feature_names()` on the `CountVectorizer` object. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/kvarada/opt/miniconda3/envs/571/lib/python3.9/site-packages/sklearn/utils/deprecation.py:87: FutureWarning: Function get_feature_names is deprecated; get_feature_names is deprecated in 1.0 and will be removed in 1.2. Please use get_feature_names_out instead.\n",
      "  warnings.warn(msg, category=FutureWarning)\n"
     ]
    }
   ],
   "source": [
    "vocab = vec.get_feature_names()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['00', '000', '01', '10', '100', '1000', '101', '11', '12', '13']"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vocab[0:10]  # first few words"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['conrad',\n",
       " 'cons',\n",
       " 'conscience',\n",
       " 'conscious',\n",
       " 'consciously',\n",
       " 'consciousness',\n",
       " 'consequence',\n",
       " 'consequences',\n",
       " 'conservative',\n",
       " 'conservatory']"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vocab[2000:2010]  # some middle words"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['00',\n",
       " 'announcement',\n",
       " 'bird',\n",
       " 'cell',\n",
       " 'conrad',\n",
       " 'depth',\n",
       " 'elite',\n",
       " 'finnish',\n",
       " 'grimy',\n",
       " 'illusions',\n",
       " 'kerr',\n",
       " 'maltin',\n",
       " 'narrates',\n",
       " 'patients',\n",
       " 'publicity',\n",
       " 'reynolds',\n",
       " 'sfx',\n",
       " 'starting',\n",
       " 'thats',\n",
       " 'vance']"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vocab[::500]  # words with a step of 500"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Model building on the dataset "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "First let's try `DummyClassifier` on the dataset. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>fit_time</th>\n",
       "      <th>score_time</th>\n",
       "      <th>test_score</th>\n",
       "      <th>train_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.001716</td>\n",
       "      <td>0.001141</td>\n",
       "      <td>0.505</td>\n",
       "      <td>0.505</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.001522</td>\n",
       "      <td>0.001093</td>\n",
       "      <td>0.505</td>\n",
       "      <td>0.505</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.001594</td>\n",
       "      <td>0.001052</td>\n",
       "      <td>0.505</td>\n",
       "      <td>0.505</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.001435</td>\n",
       "      <td>0.001063</td>\n",
       "      <td>0.505</td>\n",
       "      <td>0.505</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.001917</td>\n",
       "      <td>0.001174</td>\n",
       "      <td>0.505</td>\n",
       "      <td>0.505</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   fit_time  score_time  test_score  train_score\n",
       "0  0.001716    0.001141       0.505        0.505\n",
       "1  0.001522    0.001093       0.505        0.505\n",
       "2  0.001594    0.001052       0.505        0.505\n",
       "3  0.001435    0.001063       0.505        0.505\n",
       "4  0.001917    0.001174       0.505        0.505"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dummy = DummyClassifier()\n",
    "scores = cross_validate(dummy, X_train, y_train, return_train_score=True)\n",
    "pd.DataFrame(scores)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have a balanced dataset. So the `DummyClassifier` score is around 0.5. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Now let's try logistic regression. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>fit_time</th>\n",
       "      <th>score_time</th>\n",
       "      <th>test_score</th>\n",
       "      <th>train_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.615621</td>\n",
       "      <td>0.117341</td>\n",
       "      <td>0.847</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.595133</td>\n",
       "      <td>0.114369</td>\n",
       "      <td>0.832</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.615496</td>\n",
       "      <td>0.119625</td>\n",
       "      <td>0.842</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.634186</td>\n",
       "      <td>0.114647</td>\n",
       "      <td>0.853</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.614218</td>\n",
       "      <td>0.113491</td>\n",
       "      <td>0.839</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   fit_time  score_time  test_score  train_score\n",
       "0  0.615621    0.117341       0.847          1.0\n",
       "1  0.595133    0.114369       0.832          1.0\n",
       "2  0.615496    0.119625       0.842          1.0\n",
       "3  0.634186    0.114647       0.853          1.0\n",
       "4  0.614218    0.113491       0.839          1.0"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe_lr = make_pipeline(\n",
    "    CountVectorizer(stop_words=\"english\", max_features=10000),\n",
    "    LogisticRegression(max_iter=1000),\n",
    ")\n",
    "scores = cross_validate(pipe_lr, X_train, y_train, return_train_score=True)\n",
    "pd.DataFrame(scores)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Seems like we are overfitting. Let's optimize the hyperparameter `C`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>C</th>\n",
       "      <th>mean_train_scores</th>\n",
       "      <th>mean_cv_scores</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.001</td>\n",
       "      <td>0.83470</td>\n",
       "      <td>0.7964</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.010</td>\n",
       "      <td>0.92265</td>\n",
       "      <td>0.8456</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.100</td>\n",
       "      <td>0.98585</td>\n",
       "      <td>0.8520</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.000</td>\n",
       "      <td>1.00000</td>\n",
       "      <td>0.8426</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>10.000</td>\n",
       "      <td>1.00000</td>\n",
       "      <td>0.8376</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>100.000</td>\n",
       "      <td>1.00000</td>\n",
       "      <td>0.8350</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         C  mean_train_scores  mean_cv_scores\n",
       "0    0.001            0.83470          0.7964\n",
       "1    0.010            0.92265          0.8456\n",
       "2    0.100            0.98585          0.8520\n",
       "3    1.000            1.00000          0.8426\n",
       "4   10.000            1.00000          0.8376\n",
       "5  100.000            1.00000          0.8350"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scores_dict = {\n",
    "    \"C\": 10.0 ** np.arange(-3, 3, 1),\n",
    "    \"mean_train_scores\": list(),\n",
    "    \"mean_cv_scores\": list(),\n",
    "}\n",
    "for C in scores_dict[\"C\"]:\n",
    "    pipe_lr = make_pipeline(\n",
    "        CountVectorizer(stop_words=\"english\", max_features=10000),\n",
    "        LogisticRegression(max_iter=1000, C=C),\n",
    "    )\n",
    "    scores = cross_validate(pipe_lr, X_train, y_train, return_train_score=True)\n",
    "    scores_dict[\"mean_train_scores\"].append(scores[\"train_score\"].mean())\n",
    "    scores_dict[\"mean_cv_scores\"].append(scores[\"test_score\"].mean())\n",
    "\n",
    "results_df = pd.DataFrame(scores_dict)\n",
    "results_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The maximum validation score is 0.852 at C = 0.10 \n"
     ]
    }
   ],
   "source": [
    "optimized_C = results_df[\"C\"].iloc[np.argmax(results_df[\"mean_cv_scores\"])]\n",
    "print(\n",
    "    \"The maximum validation score is %0.3f at C = %0.2f \"\n",
    "    % (\n",
    "        np.max(results_df[\"mean_cv_scores\"]),\n",
    "        optimized_C,\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's train a model on the full training set with the optimized hyperparameter values. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(steps=[('countvectorizer',\n",
       "                 CountVectorizer(max_features=10000, stop_words='english')),\n",
       "                ('logisticregression',\n",
       "                 LogisticRegression(C=0.1, max_iter=1000))])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe_lr = make_pipeline(\n",
    "    CountVectorizer(stop_words=\"english\", max_features=10000),\n",
    "    LogisticRegression(max_iter=1000, C=optimized_C),\n",
    ")\n",
    "pipe_lr.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Examining learned coefficients "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "- The learned coefficients are exposed by the `coef_` attribute of [LogisticRegression](http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegression.html) object. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/kvarada/opt/miniconda3/envs/571/lib/python3.9/site-packages/sklearn/utils/deprecation.py:87: FutureWarning: Function get_feature_names is deprecated; get_feature_names is deprecated in 1.0 and will be removed in 1.2. Please use get_feature_names_out instead.\n",
      "  warnings.warn(msg, category=FutureWarning)\n"
     ]
    }
   ],
   "source": [
    "feature_names = np.array(pipe_lr.named_steps[\"countvectorizer\"].get_feature_names())\n",
    "coeffs = pipe_lr.named_steps[\"logisticregression\"].coef_.flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Coefficient</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>00</th>\n",
       "      <td>-0.074949</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>000</th>\n",
       "      <td>-0.083893</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>01</th>\n",
       "      <td>-0.034402</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.056493</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100</th>\n",
       "      <td>0.041633</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>zoom</th>\n",
       "      <td>-0.013299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>zooms</th>\n",
       "      <td>-0.022139</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>zorak</th>\n",
       "      <td>0.021878</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>zorro</th>\n",
       "      <td>0.130075</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>â½</th>\n",
       "      <td>0.012649</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10000 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       Coefficient\n",
       "00       -0.074949\n",
       "000      -0.083893\n",
       "01       -0.034402\n",
       "10        0.056493\n",
       "100       0.041633\n",
       "...            ...\n",
       "zoom     -0.013299\n",
       "zooms    -0.022139\n",
       "zorak     0.021878\n",
       "zorro     0.130075\n",
       "â½        0.012649\n",
       "\n",
       "[10000 rows x 1 columns]"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "word_coeff_df = pd.DataFrame(coeffs, index=feature_names, columns=[\"Coefficient\"])\n",
    "word_coeff_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Let's sort the coefficients in descending order. \n",
    "- Interpretation\n",
    "    - if $w_j > 0$ then increasing $x_{ij}$ moves us toward predicting $+1$. \n",
    "    - if $w_j < 0$ then increasing $x_{ij}$ moves us toward predicting $-1$. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Coefficient</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>excellent</th>\n",
       "      <td>0.903484</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>great</th>\n",
       "      <td>0.659922</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>amazing</th>\n",
       "      <td>0.653301</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>wonderful</th>\n",
       "      <td>0.651763</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>favorite</th>\n",
       "      <td>0.607887</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>terrible</th>\n",
       "      <td>-0.621695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>boring</th>\n",
       "      <td>-0.701030</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bad</th>\n",
       "      <td>-0.736608</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>waste</th>\n",
       "      <td>-0.799353</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>worst</th>\n",
       "      <td>-0.986970</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10000 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           Coefficient\n",
       "excellent     0.903484\n",
       "great         0.659922\n",
       "amazing       0.653301\n",
       "wonderful     0.651763\n",
       "favorite      0.607887\n",
       "...                ...\n",
       "terrible     -0.621695\n",
       "boring       -0.701030\n",
       "bad          -0.736608\n",
       "waste        -0.799353\n",
       "worst        -0.986970\n",
       "\n",
       "[10000 rows x 1 columns]"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "word_coeff_df.sort_values(by=\"Coefficient\", ascending=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The coefficients make sense!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's visualize the top 10 features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mglearn.tools.visualize_coefficients(coeffs, feature_names, n_top_features=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's explore prediction of the following new review. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "fake_review = \"It got a bit boring at times but the direction was excellent and the acting was flawless. Overall I enjoyed the movie and I highly recomment it!\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "feat_vec = pipe_lr.named_steps[\"countvectorizer\"].transform([fake_review])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<1x10000 sparse matrix of type '<class 'numpy.int64'>'\n",
       "\twith 12 stored elements in Compressed Sparse Row format>"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feat_vec"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's get prediction probability scores of the fake review. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.1718113, 0.8281887]])"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe_lr.predict_proba([fake_review])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model is 82% confident that it's a positive review. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'pos'"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe_lr.predict([fake_review])[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We can find which of the vocabulary words are present in this review:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False, False, ..., False, False, False])"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feat_vec.toarray().ravel().astype(bool)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False, False, ..., False, False, False])"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "words_in_ex = feat_vec.toarray().ravel().astype(bool)\n",
    "words_in_ex"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How many of the words are in this review?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(words_in_ex)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['acting', 'bit', 'boring', 'direction', 'enjoyed', 'excellent',\n",
       "       'flawless', 'got', 'highly', 'movie', 'overall', 'times'],\n",
       "      dtype='<U17')"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array(feature_names)[words_in_ex]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Coefficient</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>acting</th>\n",
       "      <td>-0.126498</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bit</th>\n",
       "      <td>0.390053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>boring</th>\n",
       "      <td>-0.701030</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>direction</th>\n",
       "      <td>-0.268316</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>enjoyed</th>\n",
       "      <td>0.578879</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>excellent</th>\n",
       "      <td>0.903484</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>flawless</th>\n",
       "      <td>0.113743</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>got</th>\n",
       "      <td>-0.122759</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>highly</th>\n",
       "      <td>0.582012</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>movie</th>\n",
       "      <td>-0.037942</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>overall</th>\n",
       "      <td>0.136288</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>times</th>\n",
       "      <td>0.133895</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Coefficient\n",
       "acting       -0.126498\n",
       "bit           0.390053\n",
       "boring       -0.701030\n",
       "direction    -0.268316\n",
       "enjoyed       0.578879\n",
       "excellent     0.903484\n",
       "flawless      0.113743\n",
       "got          -0.122759\n",
       "highly        0.582012\n",
       "movie        -0.037942\n",
       "overall       0.136288\n",
       "times         0.133895"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ex_df = pd.DataFrame(\n",
    "    data=coeffs[words_in_ex],\n",
    "    index=np.array(feature_names)[words_in_ex],\n",
    "    columns=[\"Coefficient\"],\n",
    ")\n",
    "ex_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's visualize how the words with positive and negative coefficients are driving the hard prediction. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mglearn.tools.visualize_coefficients(\n",
    "    coeffs[words_in_ex], np.array(feature_names)[words_in_ex], n_top_features=6\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def plot_coeff_example(feat_vect, coeffs, feature_names):\n",
    "    words_in_ex = feat_vec.toarray().ravel().astype(bool)\n",
    "\n",
    "    ex_df = pd.DataFrame(\n",
    "        data=coeffs[words_in_ex],\n",
    "        index=np.array(feature_names)[words_in_ex],\n",
    "        columns=[\"Coefficient\"],\n",
    "    )\n",
    "    return ex_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Most positive review "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Remember that you can look at the probabilities (confidence) of the classifier's prediction using the `model.predict_proba` method.\n",
    "- Can we find the messages where our classifier is most confident or least confident?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.95205899, 0.83301769, 0.9093526 , ..., 0.89247531, 0.05736279,\n",
       "       0.79360853])"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pos_probs = pipe_lr.predict_proba(X_train)[\n",
    "    :, 1\n",
    "]  # only get probabilities associated with pos class\n",
    "pos_probs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's get the index of the example where the classifier is most confident (highest `predict_proba` score for positive). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [],
   "source": [
    "most_positive = np.argmax(pos_probs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Moving beyond words is this heart breaking story of a divorce which results in a tragic custody battle over a seven year old boy.  One of \"Kramer v. Kramer\\'s\" great strengths is its screenwriter director Robert Benton, who has marvellously adapted Avery Corman\\'s novel to the big screen. He keeps things beautifully simple and most realistic, while delivering all the drama straight from the heart. His talent for telling emotional tales like this was to prove itself again with \"Places in the Heart\", where he showed, as in \"Kramer v. Kramer\", that he has a natural ability for working with children.  The picture\\'s other strong point is the splendid acting which deservedly received four of the film\\'s nine Academy Award nominations, two of them walking away winners. One of those was Dustin Hoffman (Best Actor), who is superb as frustrated business man Ted Kramer, a man who has forgotten that his wife is a person. As said wife Joanne, Meryl Streep claimed the supporting actress Oscar for a strong, sensitive portrayal of a woman who had lost herself in eight years of marriage. Also nominated was Jane Alexander for her fantastic turn as the Kramer\\'s good friend Margaret. Final word in the acting stakes must go to young Justin Henry, whose incredibly moving performance will find you choking back tears again and again, and a thoroughly deserved Oscar nomination came his way.  Brilliant also is Nestor Almendros\\' cinematography and Jerry Greenberg\\'s timely editing, while musically Henry Purcell\\'s classical piece is used to effect.  Truly this is a touching story of how a father and son come to depend on each other when their wife and mother leaves. They grow together, come to know each other and form an entirely new and wonderful relationship. Ted finds himself with new responsibilities and a new outlook on life, and slowly comes to realise why Joanne had to go.  Certainly if nothing else, \"Kramer v. Kramer\" demonstrates that nobody wins when it comes to a custody battle over a young child, especially not the child himself.  Saturday, June 10, 1995 - T.V.  Strong drama from Avery Corman\\'s novel about the heartache of a custody battle between estranged parents who both feel they have the child\\'s best interests at heart. Aside from a superb screenplay and amazingly controlled direction, both from Robert Benton, it\\'s the superlative cast that make this picture such a winner.  Hoffman is brilliant as Ted Kramer, the man torn between his toppling career and the son whom he desperately wants to keep. Excellent too is Streep as the woman lost in eight years of marriage who had to get out before she faded to nothing as a person. In support of these two is a very strong Jane Alexander as mutual friend Margaret, an outstanding Justin Henry as the boy caught in the middle, and a top cast of extras.  This highly emotional, heart rending drama more than deserved it\\'s 1979 Academy Awards for best film, best actor (Hoffman) and best supporting actress (Streep).  Wednesday, February 28, 1996 - T.V.'"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train.iloc[most_positive]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True target: pos\n",
      "\n",
      "Predicted target: pos\n",
      "\n",
      "Prediction probability: 1.0000\n"
     ]
    }
   ],
   "source": [
    "print(\"True target: %s\\n\" % (y_train.iloc[most_positive]))\n",
    "print(\"Predicted target: %s\\n\" % (pipe_lr.predict(X_train.iloc[[most_positive]])[0]))\n",
    "print(\"Prediction probability: %0.4f\" % (pos_probs[most_positive]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's examine the features associated with the review. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "feat_vec = pipe_lr.named_steps[\"countvectorizer\"].transform(\n",
    "    X_train.iloc[[most_positive]]\n",
    ")\n",
    "words_in_ex = feat_vec.toarray().ravel().astype(bool)\n",
    "mglearn.tools.visualize_coefficients(\n",
    "    coeffs[words_in_ex], np.array(feature_names)[words_in_ex], n_top_features=20\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The review has both positive and negative words but the words with **positive** coefficients win in this case! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Most negative review "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.04794101, 0.16698231, 0.0906474 , ..., 0.10752469, 0.94263721,\n",
       "       0.20639147])"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "neg_probs = pipe_lr.predict_proba(X_train)[\n",
    "    :, 0\n",
    "]  # only get probabilities associated with pos class\n",
    "neg_probs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "most_negative = np.argmax(neg_probs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Review: 36555    I made the big mistake of actually watching this whole movie a few nights ago. God I'm still trying to recover. This movie does not even deserve a 1.4 average. IMDb needs to have 0 vote ratings po...\n",
      "Name: review_pp, dtype: object\n",
      "\n",
      "True target: neg\n",
      "\n",
      "Predicted target: neg\n",
      "\n",
      "Prediction probability: 0.0000\n"
     ]
    }
   ],
   "source": [
    "print(\"Review: %s\\n\" % (X_train.iloc[[most_negative]]))\n",
    "print(\"True target: %s\\n\" % (y_train.iloc[most_negative]))\n",
    "print(\"Predicted target: %s\\n\" % (pipe_lr.predict(X_train.iloc[[most_negative]])[0]))\n",
    "print(\"Prediction probability: %0.4f\" % (pos_probs[most_negative]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "feat_vec = pipe_lr.named_steps[\"countvectorizer\"].transform(\n",
    "    X_train.iloc[[most_negative]]\n",
    ")\n",
    "words_in_ex = feat_vec.toarray().ravel().astype(bool)\n",
    "mglearn.tools.visualize_coefficients(\n",
    "    coeffs[words_in_ex], np.array(feature_names)[words_in_ex], n_top_features=20\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The review has both positive and negative words but the words with negative coefficients win in this case! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### ❓❓ Questions for you"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "#### Question for you to ponder on \n",
    "\n",
    "- Is it possible to identify most important features using $k$-NNs? What about decision trees?  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "<br><br><br><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Summary of linear models \n",
    "\n",
    "- Linear regression is a linear model for regression whereas logistic regression is a linear model for classification. \n",
    "- Both these models learn one coefficient per feature, plus an intercept. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Main hyperparameters \n",
    "- The main hyperparameter is the \"regularization\" hyperparameter controlling the fundamental tradeoff. \n",
    "    - Logistic Regression: `C`\n",
    "    - Linear SVM: `C` \n",
    "    - Ridge: `alpha`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Interpretation of coefficients in linear models \n",
    "- the $j$th coefficient tells us how feature $j$ affects the prediction\n",
    "- if $w_j > 0$ then increasing $x_{ij}$ moves us toward predicting $+1$\n",
    "- if $w_j < 0$ then increasing $x_{ij}$ moves us toward prediction $-1$\n",
    "- if $w_j == 0$ then the feature is not used in making a prediction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Strengths of linear models \n",
    "\n",
    "- Fast to train and predict\n",
    "- Scale to large datasets and work well with sparse data \n",
    "- Relatively easy to understand and interpret the predictions\n",
    "- Perform well when there is a large number of features "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Limitations of linear models \n",
    "\n",
    "- Is your data \"linearly separable\"? Can you draw a hyperplane between these datapoints that separates them with 0 error. \n",
    "    - If the training examples can be separated by a linear decision rule, they are **linearly separable**.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "A few questions you might be thinking about\n",
    "- How often the real-life data is linearly separable?\n",
    "- Is the following XOR function linearly separable?  \n",
    "\n",
    "| $$x_1$$ | $$x_2$$ | target|\n",
    "|---------|---------|---------|\n",
    "| 0 | 0  | 0|\n",
    "| 0 | 1  | 1|\n",
    "| 1 | 0  | 1|\n",
    "| 1 | 1  | 0|    \n",
    "\n",
    "- Are linear classifiers very limiting because of this?     "
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