UCI_demo.ipynb

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   "source": [
    "# Missing data imputation using optimal transport\n",
    "\n",
    "In this notebook, we will show how to use optimal transport to impute missing values in an incomplete dataset.\n",
    "\n",
    "The methods we will use are described in the following paper:\n",
    "\n",
    "B. Muzellec, J. Josse, C. Boyer, M. Cuturi, [Missing Data Imputation using Optimal Transport](https://arxiv.org/pdf/2002.03860.pdf)."
   ]
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Imports and installs"
   ],
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   }
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "outputs": [
    {
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     "text": [
      "Requirement already satisfied: pot in /Users/boris/opt/anaconda3/lib/python3.7/site-packages (0.6.0)\r\n",
      "Requirement already satisfied: numpy in /Users/boris/opt/anaconda3/lib/python3.7/site-packages (from pot) (1.18.1)\r\n",
      "Requirement already satisfied: cython in /Users/boris/opt/anaconda3/lib/python3.7/site-packages (from pot) (0.29.15)\r\n",
      "Requirement already satisfied: scipy in /Users/boris/opt/anaconda3/lib/python3.7/site-packages (from pot) (1.4.1)\r\n",
      "Requirement already satisfied: geomloss in /Users/boris/opt/anaconda3/lib/python3.7/site-packages (0.2.3)\r\n",
      "Requirement already satisfied: numpy in /Users/boris/opt/anaconda3/lib/python3.7/site-packages (from geomloss) (1.18.1)\r\n"
     ]
    }
   ],
   "source": [
    "# Ignore this cell if the corresponding packages are already installed\n",
    "\n",
    "!pip install pot\n",
    "!pip install geomloss"
   ],
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     "name": "#%%\n"
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   "cell_type": "code",
   "execution_count": 2,
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   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import numpy as np\n",
    "\n",
    "from sklearn.preprocessing import scale\n",
    "from sklearn.experimental import enable_iterative_imputer\n",
    "from sklearn.impute import SimpleImputer, IterativeImputer\n",
    "\n",
    "import os\n",
    "\n",
    "from geomloss import SamplesLoss\n",
    "\n",
    "from imputers import OTimputer, RRimputer\n",
    "\n",
    "from utils import *\n",
    "from data_loaders import dataset_loader\n",
    "from softimpute import softimpute, cv_softimpute\n",
    "\n",
    "import logging\n",
    "logger = logging.getLogger()\n",
    "logger.setLevel(logging.INFO)\n",
    "logging.debug(\"test\")\n",
    "\n",
    "torch.set_default_tensor_type('torch.DoubleTensor')"
   ],
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    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
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   "cell_type": "markdown",
   "source": [
    "## Data loading\n",
    "\n",
    "The dataset loader utilities assume there is a \"datasets/\" folder in the current directory."
   ],
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    "pycharm": {
     "name": "#%% md\n"
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  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "outputs": [],
   "source": [
    "if not os.path.isdir(\"datasets\"):\n",
    "    os.mkdir(\"datasets\")"
   ],
   "metadata": {
    "collapsed": false,
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     "name": "#%%\n"
    }
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  },
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   "cell_type": "markdown",
   "source": [
    "Load the data and whiten it.\n",
    "In a real missing data situation, the mean and std would have to be estimated on non-missing data."
   ],
   "metadata": {
    "collapsed": false,
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     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "outputs": [],
   "source": [
    "ground_truth = scale(dataset_loader(\"wine\")) # \"wine\" can be replaced with any of the datasets\n",
    "                                             # supported by dataset_loader (see data_loaders.py)\n",
    "\n",
    "X_true = torch.from_numpy(ground_truth)"
   ],
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     "name": "#%%\n"
    }
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   "cell_type": "markdown",
   "source": [
    "## Missing data generation\n",
    "\n",
    "Let's now simulate missing data. We will assume that the data is missing completely at random (MCAR) with a 50% probability.\n",
    "Additional MAR and MNAR missing data mechanisms are available in utils.py."
   ],
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     "name": "#%% md\n"
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   "execution_count": 5,
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "\n",
    "p = 0.5\n",
    "\n",
    "mask = np.random.rand(*ground_truth.shape) < p #True for missing values, false for others\n",
    "x_miss = np.copy(ground_truth)\n",
    "\n",
    "x_miss[mask] = np.nan\n",
    "X_miss = torch.from_numpy(x_miss)"
   ],
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     "name": "#%%\n"
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  },
  {
   "cell_type": "markdown",
   "source": [
    "## Hyperparameters"
   ],
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   "cell_type": "code",
   "execution_count": 6,
   "outputs": [],
   "source": [
    "n, d = X_miss.shape\n",
    "batchsize = 128 # If the batch size is larger than half the dataset's size,\n",
    "                # it will be redefined in the imputation methods.\n",
    "lr = 1e-2\n",
    "epsilon = pick_epsilon(X_miss) # Set the regularization parameter as a multiple of the median distance, as per the paper."
   ],
   "metadata": {
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    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Sinkhorn imputation (Algorithm 1)"
   ],
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    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "outputs": [],
   "source": [
    "sk_imputer = OTimputer(eps=epsilon, batchsize=batchsize, lr=lr, niter=2000)"
   ],
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    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
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  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "outputs": [
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     "name": "stderr",
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     "text": [
      "INFO:root:Batchsize larger that half size = 89. Setting batchsize to 64.\n",
      "INFO:root:batchsize = 64, epsilon = 0.2697\n",
      "INFO:root:Iteration 0:\t Loss: 1.5279\t Validation MAE: 0.8615\tRMSE: 1.0539\n",
      "INFO:root:Iteration 500:\t Loss: 1.0651\t Validation MAE: 0.6361\tRMSE: 0.8679\n",
      "INFO:root:Iteration 1000:\t Loss: 0.9501\t Validation MAE: 0.6311\tRMSE: 0.8674\n",
      "INFO:root:Iteration 1500:\t Loss: 1.0874\t Validation MAE: 0.6343\tRMSE: 0.8725\n"
     ]
    }
   ],
   "source": [
    "sk_imp, sk_maes, sk_rmses = sk_imputer.fit_transform(X_miss, verbose=True, report_interval=500, X_true=X_true)"
   ],
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  },
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   "source": [
    "## Round-robin imputation (Algorithm 3)\n",
    "\n",
    "Round-robin imputation models iteratively impute each variable using all the other variables.\n",
    "The imputation is performed according to an optimal transport criterion, as in Algorithm 3 in the paper.\n",
    "Any model can be used to perform the variable imputation. It is even possible to specify one type of model per variable\n",
    "(e.g. predict a variable with a linear model, and an other with an MLP), as long as those models gave trainable parameters.\n",
    "\n",
    "We give here two examples. In the first, variables are predicted using linear models, and in the second using a MLP.\n",
    "\n",
    "Note that even if each variable has an associated model of the same type as the others,\n",
    "those models have distinct sets of parameters."
   ],
   "metadata": {
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    "pycharm": {
     "name": "#%% md\n"
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   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Linear round-robin"
   ],
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    "collapsed": false,
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     "name": "#%% md\n"
    }
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  },
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   "execution_count": 9,
   "outputs": [],
   "source": [
    "#Create the imputation models\n",
    "d_ = d - 1\n",
    "models = {}\n",
    "\n",
    "for i in range(d):\n",
    "    models[i] = nn.Linear(d_, 1)\n",
    "\n",
    "#Create the imputer\n",
    "lin_rr_imputer = RRimputer(models, eps=epsilon, lr=lr)"
   ],
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    "pycharm": {
     "name": "#%%\n"
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  {
   "cell_type": "code",
   "execution_count": 10,
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:root:Batchsize larger that half size = 89. Setting batchsize to 64.\n",
      "INFO:root:Iteration 0:\t Loss: 1.7705\tValidation MAE: 0.7467\tRMSE:  0.9541\n",
      "INFO:root:Iteration 1:\t Loss: 1.3344\tValidation MAE: 0.7117\tRMSE:  0.9366\n",
      "INFO:root:Iteration 2:\t Loss: 1.3620\tValidation MAE: 0.6858\tRMSE:  0.9108\n",
      "INFO:root:Iteration 3:\t Loss: 1.3318\tValidation MAE: 0.6802\tRMSE:  0.8995\n",
      "INFO:root:Iteration 4:\t Loss: 1.3122\tValidation MAE: 0.6704\tRMSE:  0.8923\n",
      "INFO:root:Iteration 5:\t Loss: 1.2849\tValidation MAE: 0.6709\tRMSE:  0.8933\n",
      "INFO:root:Iteration 6:\t Loss: 1.2932\tValidation MAE: 0.6682\tRMSE:  0.8883\n",
      "INFO:root:Iteration 7:\t Loss: 1.2972\tValidation MAE: 0.6696\tRMSE:  0.8919\n",
      "INFO:root:Iteration 8:\t Loss: 1.3920\tValidation MAE: 0.6676\tRMSE:  0.8886\n",
      "INFO:root:Iteration 9:\t Loss: 1.2369\tValidation MAE: 0.6703\tRMSE:  0.8927\n",
      "INFO:root:Early stopping criterion not reached\n"
     ]
    }
   ],
   "source": [
    "lin_imp, lin_maes, lin_rmses = lin_rr_imputer.fit_transform(X_miss, verbose=True, X_true=X_true)"
   ],
   "metadata": {
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    "pycharm": {
     "name": "#%%\n"
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   "source": [
    "### MLP round-robin"
   ],
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     "name": "#%% md\n"
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  {
   "cell_type": "code",
   "execution_count": 11,
   "outputs": [],
   "source": [
    "#Create the imputation models\n",
    "d_ = d - 1\n",
    "models = {}\n",
    "\n",
    "for i in range(d):\n",
    "    models[i] = nn.Sequential(nn.Linear(d_, 2 * d_),\n",
    "                              nn.ReLU(),\n",
    "                              nn.Linear(2 * d_, d_),\n",
    "                              nn.ReLU(),\n",
    "                              nn.Linear(d_, 1))\n",
    "\n",
    "#Create the imputer\n",
    "mlp_rr_imputer = RRimputer(models, eps=epsilon, lr=lr)"
   ],
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    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
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  {
   "cell_type": "code",
   "execution_count": 12,
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:root:Batchsize larger that half size = 89. Setting batchsize to 64.\n",
      "INFO:root:Iteration 0:\t Loss: 1.2783\tValidation MAE: 0.6612\tRMSE:  0.8848\n",
      "INFO:root:Iteration 1:\t Loss: 1.2325\tValidation MAE: 0.6445\tRMSE:  0.8709\n",
      "INFO:root:Iteration 2:\t Loss: 1.3013\tValidation MAE: 0.6438\tRMSE:  0.8773\n",
      "INFO:root:Iteration 3:\t Loss: 1.2987\tValidation MAE: 0.6464\tRMSE:  0.8824\n",
      "INFO:root:Iteration 4:\t Loss: 1.6957\tValidation MAE: 0.6438\tRMSE:  0.8851\n",
      "INFO:root:Iteration 5:\t Loss: 1.2492\tValidation MAE: 0.6536\tRMSE:  0.8967\n",
      "INFO:root:Iteration 6:\t Loss: 1.2932\tValidation MAE: 0.6582\tRMSE:  0.8995\n",
      "INFO:root:Iteration 7:\t Loss: 1.2198\tValidation MAE: 0.6636\tRMSE:  0.9100\n",
      "INFO:root:Iteration 8:\t Loss: 1.2143\tValidation MAE: 0.6684\tRMSE:  0.9153\n",
      "INFO:root:Iteration 9:\t Loss: 1.3173\tValidation MAE: 0.6648\tRMSE:  0.9102\n",
      "INFO:root:Early stopping criterion not reached\n"
     ]
    }
   ],
   "source": [
    "mlp_imp, mlp_maes, mlp_rmses = mlp_rr_imputer.fit_transform(X_miss, verbose=True, X_true=X_true)"
   ],
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    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
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   "cell_type": "markdown",
   "source": [
    "## Baselines\n",
    "\n",
    "Let's compare OT imputations to some baselines. As in the paper, we consider the following baselines: (i) mean imputation, (ii) iterated conditional ridge regression and (iii) softimpute."
   ],
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   "cell_type": "code",
   "execution_count": 13,
   "outputs": [],
   "source": [
    "# Imputation by the means\n",
    "mean_imp = SimpleImputer().fit_transform(x_miss)\n",
    "mean_mae = MAE(mean_imp, ground_truth, mask)\n",
    "mean_rmse = RMSE(mean_imp, ground_truth, mask)\n",
    "\n",
    "# ICE\n",
    "ice_imp = IterativeImputer(random_state=0, max_iter=50).fit_transform(x_miss)\n",
    "ice_mae = MAE(ice_imp, ground_truth, mask)\n",
    "ice_rmse = RMSE(ice_imp, ground_truth, mask)\n",
    "\n",
    "# Softimpute\n",
    "cv_error, grid_lambda = cv_softimpute(x_miss, grid_len=15)\n",
    "lbda = grid_lambda[np.argmin(cv_error)]\n",
    "soft_imp = softimpute((x_miss), lbda)[1]\n",
    "\n",
    "soft_mae = MAE(soft_imp, ground_truth, mask)\n",
    "soft_rmse = RMSE(soft_imp, ground_truth, mask)"
   ],
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    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Comparison plots"
   ],
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    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(constrained_layout=True)\n",
    "npoints = len(sk_maes)\n",
    "\n",
    "ax.plot(np.linspace(0, 1, npoints) * npoints, sk_maes, label='Sinkhorn')\n",
    "ax.set_xticks(np.linspace(0, npoints, 6))\n",
    "ax.set_xlabel('# Sinkhorn iterations')\n",
    "\n",
    "ax.hlines(y=mean_mae, xmin=0, xmax=npoints, label=\"Means\", ls = '--', color='black')\n",
    "ax.hlines(y=ice_mae, xmin=0, xmax=npoints, label=\"ICE\", ls = '--', color='m')\n",
    "ax.hlines(y=soft_mae, xmin=0, xmax=npoints, label=\"Softimpute\", ls = '--', color='c')\n",
    "\n",
    "secax = ax.secondary_xaxis('top', functions=(lambda x: x * len(lin_maes) / npoints, lambda x: x * npoints / len(lin_maes)))\n",
    "secax.set_xlabel('# RR iterations')\n",
    "\n",
    "ax.plot(np.linspace(0, 1, len(lin_maes)) * npoints, lin_maes, label='Linear RR')\n",
    "ax.plot(np.linspace(0, 1, len(mlp_maes)) * npoints, mlp_maes, label='MLP RR')\n",
    "\n",
    "ax.set_ylabel('MAE')\n",
    "plt.legend()\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(constrained_layout=True)\n",
    "npoints = len(sk_rmses)\n",
    "\n",
    "ax.plot(np.linspace(0, 1, npoints) * npoints, sk_rmses, label='Sinkhorn')\n",
    "ax.set_xticks(np.linspace(0, npoints, 6))\n",
    "ax.set_xlabel('# Sinkhorn iterations')\n",
    "\n",
    "ax.hlines(y=mean_rmse, xmin=0, xmax=npoints, label=\"Means\", ls = '--', color='black')\n",
    "ax.hlines(y=ice_rmse, xmin=0, xmax=npoints, label=\"ICE\", ls = '--', color='m')\n",
    "ax.hlines(y=soft_rmse, xmin=0, xmax=npoints, label=\"Softimpute\", ls = '--', color='c')\n",
    "\n",
    "secax = ax.secondary_xaxis('top', functions=(lambda x: x * len(lin_maes) / npoints, lambda x: x * npoints/ len(lin_maes)))\n",
    "secax.set_xlabel('# RR iterations')\n",
    "\n",
    "ax.plot(np.linspace(0, 1, len(lin_rmses)) * npoints, lin_rmses, label='Linear RR')\n",
    "ax.plot(np.linspace(0, 1, len(mlp_maes)) * npoints, mlp_rmses, label='MLP RR')\n",
    "\n",
    "ax.set_ylabel('RMSE')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}