FireAI_003_LinearRegressor.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x=[10 11 12 13 14 15 16 17 18 19]\n",
      "noise y=[23.7398643  25.99672892 28.9507954  28.5841992  30.88585245 31.87256307\n",
      " 34.47408176 34.34652526 39.83674872 40.82204375]\n",
      "target y=[23.9 25.7 27.5 29.3 31.1 32.9 34.7 36.5 38.3 40.1]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0xe4f6588>]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 简单线性回归模型：因变量和自变量之间呈现简单的直线关系\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "x=np.arange(10,20) # 自变量，随便定义的\n",
    "\n",
    "error=np.random.normal(size=x.shape)\n",
    "y=1.8*x+5.9+error # 添加随机数作为噪音\n",
    "print('x={}'.format(x))\n",
    "print('noise y={}'.format(y))\n",
    "print('target y={}'.format(1.8*x+5.9))\n",
    "\n",
    "plt.scatter(x,y)\n",
    "plt.plot(x,1.8*x+5.9,'-r') # 绘制的是红色的直线"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x first 5: [ 9.94553639 11.67430807 12.34664703 11.69965383 15.51851188],\n",
      "x last 5: [104.96860647 105.5657788  107.39973957 109.13188006 107.11399729]\n",
      "train set first 3: [(87.14423520405674, 167.36573263695115), (55.67781082162659, 99.22823777086437), (66.59394694856373, 132.76688712312875)], last 3: [(101.17645506359409, 192.5625947080063), (84.26081861492051, 140.24466883845), (25.045565547096164, 30.8008361424697)]\n",
      "test set first 3: [(70.59406981304555, 119.31318224915739), (57.91939805734182, 92.13834259220599), (96.47990086803438, 179.5012882066724)], last 3: [(102.0058216600241, 201.04210881463908), (18.172421360793678, 47.04372291312748), (104.96860647152728, 222.13041948920244)]\n",
      "X_train first 3: [[87.1442352 ]\n",
      " [55.67781082]\n",
      " [66.59394695]]\n",
      "y_train first 3: [[167.36573264]\n",
      " [ 99.22823777]\n",
      " [132.76688712]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ***************使用随机数据来构建简单线性回归器**********************************\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "# %matplotlib inline\n",
    "np.random.seed(37) # 使得每次运行得到的随机数都一样\n",
    "\n",
    "# 第一部分：准备数据集\n",
    "# 一般的，数据集可以放置在一个专门的txt，或csv文件中，此处我自己创造一些数据\n",
    "x=np.arange(10,110) \n",
    "x_shift=np.random.normal(size=x.shape)\n",
    "x=x+x_shift # 构建的x含有100个数，通过在整数点引入偏差得到\n",
    "print('x first 5: {},\\nx last 5: {}'.format(x[:5],x[-5:]))\n",
    "\n",
    "error=np.random.normal(size=x.shape)*15 # 构建误差作为噪音，*15是扩大噪音的影响\n",
    "y=1.8*x+5.9+error\n",
    "plt.scatter(x,y) # 可以查看生成的数据集的分布情况\n",
    "\n",
    "# 要从这100个随机选择80个点来train，剩下的20个点来test\n",
    "# 最简单的方法是调用下面的train_test_split函数\n",
    "dataset=[(i,j) for i,j in zip(x,y)]\n",
    "from sklearn.model_selection import train_test_split\n",
    "train_set,test_set=train_test_split(dataset,test_size=0.2,random_state=37)\n",
    "print('train set first 3: {}, last 3: {}'.format(train_set[:3],train_set[-3:]))\n",
    "print('test set first 3: {}, last 3: {}'.format(test_set[:3],test_set[-3:]))\n",
    "\n",
    "# 第二种方法：也可以自己先shuffle,再随机选取\n",
    "# np.random.shuffle(dataset) # 乱序排列\n",
    "# train_set,test_set=dataset[:80],dataset[80:] \n",
    "# print('train set first 3: {}, last 3: {}'.format(train_set[:3],train_set[-3:]))\n",
    "# print('test set first 3: {}, last 3: {}'.format(test_set[:3],test_set[-3:]))\n",
    "\n",
    "X_train=np.array([i for (i,j) in train_set]).reshape(-1,1) # 后面的fit需要先reshape\n",
    "y_train=np.array([j for (i,j) in train_set]).reshape(-1,1)\n",
    "X_test= np.array([i for (i,j) in test_set]).reshape(-1,1)\n",
    "y_test= np.array([j for (i,j) in test_set]).reshape(-1,1)\n",
    "print('X_train first 3: {}'.format(X_train[:3]))\n",
    "print('y_train first 3: {}'.format(y_train[:3]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x126b2f60>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 第二部分：使用train set进行模型训练\n",
    "from sklearn import linear_model\n",
    "\n",
    "linear_regressor=linear_model.LinearRegression() # 创建线性回归器对象\n",
    "linear_regressor.fit(X_train,y_train) # 使用训练数据集训练该回归器对象\n",
    "\n",
    "# 查看拟合结果\n",
    "y_predict=linear_regressor.predict(X_train) # 使用训练后的回归器对象来拟合训练数据\n",
    "plt.figure()\n",
    "plt.scatter(X_train,y_train)\n",
    "plt.plot(X_train,y_predict,'-b',linewidth=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x124dc278>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 用训练好的模型计算测试集的数据，看是否能得到准确值\n",
    "y_predict_test=linear_regressor.predict(X_test)\n",
    "plt.figure()\n",
    "plt.scatter(X_test,y_test)\n",
    "plt.plot(X_test,y_predict_test,'-b',linewidth=3)\n",
    "plt.scatter(X_test,y_predict_test,color='black',marker='x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "平均绝对误差：11.98\n",
      "均方误差MSE：211.52\n",
      "中位数绝对误差：12.35\n",
      "解释方差分：0.93\n",
      "R方得分：0.92\n"
     ]
    }
   ],
   "source": [
    "# 使用评价指标来评估模型的好坏\n",
    "import sklearn.metrics as metrics\n",
    "print('平均绝对误差：{}'.format(\n",
    "    round(metrics.mean_absolute_error(y_predict_test,y_test),2)))\n",
    "print('均方误差MSE：{}'.format(\n",
    "    round(metrics.mean_squared_error(y_predict_test,y_test),2)))\n",
    "print('中位数绝对误差：{}'.format(\n",
    "    round(metrics.median_absolute_error(y_predict_test,y_test),2)))\n",
    "print('解释方差分：{}'.format(\n",
    "    round(metrics.explained_variance_score(y_predict_test,y_test),2)))\n",
    "print('R方得分：{}'.format(\n",
    "    round(metrics.r2_score(y_predict_test,y_test),2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "直线的截距: [9.50824666]\n",
      "直线的系数（斜率）: [[1.71905515]]\n",
      "用线性模型计算的值：[[215.79486427]]\n",
      "直线方程计算的值：[[215.79486427]]\n",
      "pickle加载后的模型计算结果：[[215.79486427]]\n",
      "joblib加载后的模型计算结果：[[215.79486427]]\n"
     ]
    }
   ],
   "source": [
    "# 回归模型的保存和加载\n",
    "\n",
    "# 在保存之前先看一下模型的内部参数，主要为两项，截距和系数\n",
    "print('直线的截距: {}'.format(linear_regressor.intercept_)) #这是截距\n",
    "print('直线的系数（斜率）: {}'.format(linear_regressor.coef_)) #这系数，对应于本项目的直线斜率\n",
    "y_value=linear_regressor.predict([[120]])\n",
    "print('用线性模型计算的值：{}'\n",
    "      .format(y_value)) # 这两个print的结果应该是一样的\n",
    "print('直线方程计算的值：{}'\n",
    "      .format(linear_regressor.coef_*120+linear_regressor.intercept_)) \n",
    "\n",
    "save_path='d:/Models/LinearRegressor_v1.txt'\n",
    "\n",
    "# 第一种方法，pickle\n",
    "import pickle\n",
    "s=pickle.dumps(linear_regressor) # 模型保存\n",
    "loaded_classifier=pickle.loads(s) # 模型加载\n",
    "y_value=loaded_classifier.predict([[120]])\n",
    "print('pickle加载后的模型计算结果：{}'.format(y_value))\n",
    "\n",
    "# 第二种方法：joblib\n",
    "from sklearn.externals import joblib\n",
    "joblib.dump(linear_regressor,save_path) # 模型保存到文件中\n",
    "loaded_classifier2=joblib.load(save_path)\n",
    "y_value=loaded_classifier2.predict([[120]])\n",
    "print('joblib加载后的模型计算结果：{}'.format(y_value))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}