examples/cd_model_unc_cifar10_wine.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Model uncertainty based drift detection on CIFAR-10 and Wine-Quality datasets\n",
    "\n",
    "### Method\n",
    "\n",
    "Model-uncertainty drift detectors aim to directly detect drift that's likely to effect the performance of a model of interest. The approach is to test for change in the number of instances falling into regions of the input space on which the model is uncertain in its predictions. For each instance in the reference set the detector obtains the model's prediction and some associated notion of uncertainty. For example for a classifier this may be the entropy of the predicted label probabilities or for a regressor with dropout layers [dropout Monte Carlo](http://proceedings.mlr.press/v48/gal16.pdf) can be used to provide a notion of uncertainty. The same is done for the test set and if significant differences in uncertainty are detected (via a Kolmogorov-Smirnoff test) then drift is flagged. \n",
    "\n",
    "It is important that the detector uses a reference set that is disjoint from the model's training set (on which the model's confidence may be higher).\n",
    "\n",
    "\n",
    "### Backend\n",
    "\n",
    "For models that require batch evaluation both **PyTorch** and **TensorFlow** frameworks are supported. Alibi Detect does however not install PyTorch for you. \n",
    "Check the [PyTorch docs](https://pytorch.org/) how to do this."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Classifier uncertainty based drift detection\n",
    "\n",
    "We start by demonstrating how to leverage model uncertainty to detect malicious drift when the model of interest is a classifer.\n",
    "\n",
    "#### Dataset\n",
    "\n",
    "[CIFAR10](https://www.cs.toronto.edu/~kriz/cifar.html) consists of 60,000 32 by 32 RGB images equally distributed over 10 classes. We evaluate the drift detector on the CIFAR-10-C dataset ([Hendrycks & Dietterich, 2019](https://arxiv.org/abs/1903.12261)). The instances in\n",
    "CIFAR-10-C have been corrupted and perturbed by various types of noise, blur, brightness etc. at different levels of severity, leading to a gradual decline in the classification model performance. We also check for drift against the original test set with class imbalances. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import os\n",
    "import tensorflow as tf\n",
    "import torch\n",
    "from torch import nn\n",
    "\n",
    "from alibi_detect.cd import ClassifierUncertaintyDrift, RegressorUncertaintyDrift\n",
    "from alibi_detect.models.tensorflow.resnet import scale_by_instance\n",
    "from alibi_detect.utils.fetching import fetch_tf_model, fetch_detector\n",
    "from alibi_detect.utils.saving import save_detector, load_detector\n",
    "from alibi_detect.datasets import fetch_cifar10c, corruption_types_cifar10c\n",
    "from alibi_detect.models.pytorch.trainer import trainer\n",
    "from alibi_detect.cd.utils import encompass_batching"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Original CIFAR-10 data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "(X_train, y_train), (X_test, y_test) = tf.keras.datasets.cifar10.load_data()\n",
    "X_train = X_train.astype('float32') / 255\n",
    "X_test = X_test.astype('float32') / 255\n",
    "y_train = y_train.astype('int64').reshape(-1,)\n",
    "y_test = y_test.astype('int64').reshape(-1,)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For CIFAR-10-C, we can select from the following corruption types at 5 severity levels:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['brightness', 'contrast', 'defocus_blur', 'elastic_transform', 'fog', 'frost', 'gaussian_blur', 'gaussian_noise', 'glass_blur', 'impulse_noise', 'jpeg_compression', 'motion_blur', 'pixelate', 'saturate', 'shot_noise', 'snow', 'spatter', 'speckle_noise', 'zoom_blur']\n"
     ]
    }
   ],
   "source": [
    "corruptions = corruption_types_cifar10c()\n",
    "print(corruptions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's pick a subset of the corruptions at corruption level 5. Each corruption type consists of perturbations on all of the original test set images."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "corruption = ['gaussian_noise', 'motion_blur', 'brightness', 'pixelate']\n",
    "X_corr, y_corr = fetch_cifar10c(corruption=corruption, severity=5, return_X_y=True)\n",
    "X_corr = X_corr.astype('float32') / 255"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We split the original test set in a reference dataset and a dataset which should not be rejected under the no-change null *H<sub>0</sub>*. We also split the corrupted data by corruption type:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(5000, 32, 32, 3) (5000, 32, 32, 3)\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(0)\n",
    "n_test = X_test.shape[0]\n",
    "idx = np.random.choice(n_test, size=n_test // 2, replace=False)\n",
    "idx_h0 = np.delete(np.arange(n_test), idx, axis=0)\n",
    "X_ref,y_ref = X_test[idx], y_test[idx]\n",
    "X_h0, y_h0 = X_test[idx_h0], y_test[idx_h0]\n",
    "print(X_ref.shape, X_h0.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Class Ref H0\n",
      "0     472 528\n",
      "1     510 490\n",
      "2     498 502\n",
      "3     492 508\n",
      "4     501 499\n",
      "5     495 505\n",
      "6     493 507\n",
      "7     501 499\n",
      "8     516 484\n",
      "9     522 478\n"
     ]
    }
   ],
   "source": [
    "# check that the classes are more or less balanced\n",
    "classes, counts_ref = np.unique(y_ref, return_counts=True)\n",
    "counts_h0 = np.unique(y_h0, return_counts=True)[1]\n",
    "print('Class Ref H0')\n",
    "for cl, cref, ch0 in zip(classes, counts_ref, counts_h0):\n",
    "    assert cref + ch0 == n_test // 10\n",
    "    print('{}     {} {}'.format(cl, cref, ch0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_corr = len(corruption)\n",
    "X_c = [X_corr[i * n_test:(i + 1) * n_test] for i in range(n_corr)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can visualise the same instance for each corruption type:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "tags": [
     "hide_input"
    ]
   },
   "outputs": [
    {
     "data": {
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       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "i = 1\n",
    "\n",
    "n_test = X_test.shape[0]\n",
    "plt.title('Original')\n",
    "plt.axis('off')\n",
    "plt.imshow(X_test[i])\n",
    "plt.show()\n",
    "for _ in range(len(corruption)):\n",
    "    plt.title(corruption[_])\n",
    "    plt.axis('off')\n",
    "    plt.imshow(X_corr[n_test * _+ i])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also verify that the performance of a classification model on CIFAR-10 drops significantly on this perturbed dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test set accuracy:\n",
      "Original 0.9278\n",
      "gaussian_noise 0.2208\n",
      "motion_blur 0.6339\n",
      "brightness 0.8913\n",
      "pixelate 0.3666\n"
     ]
    }
   ],
   "source": [
    "dataset = 'cifar10'\n",
    "model = 'resnet32'\n",
    "clf = fetch_tf_model(dataset, model)\n",
    "acc = clf.evaluate(scale_by_instance(X_test), y_test, batch_size=128, verbose=0)[1]\n",
    "print('Test set accuracy:')\n",
    "print('Original {:.4f}'.format(acc))\n",
    "clf_accuracy = {'original': acc}\n",
    "for _ in range(len(corruption)):\n",
    "    acc = clf.evaluate(scale_by_instance(X_c[_]), y_test, batch_size=128, verbose=0)[1]\n",
    "    clf_accuracy[corruption[_]] = acc\n",
    "    print('{} {:.4f}'.format(corruption[_], acc))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given the drop in performance, it is important that we detect the harmful data drift!\n",
    "\n",
    "#### Detect drift\n",
    "\n",
    "Unlike many other approaches we needn't specify a dimension-reducing preprocessing step as the detector operates directly on the data as it is input to the model of interest. In fact, the two-stage projection  input -> prediction -> uncertainty can be thought of as the projection from the input space onto the real line, ready to perform the test.\n",
    "\n",
    "We simply pass the model to the detector and inform it that the predictions should be interpreted as 'probs' rather than 'logits' (i.e. a softmax has already been applied). By default `uncertainty_type='entropy'` is used as the notion of uncertainty for classifier predictions, however `uncertainty_type='margin'` can be specified to deem the classifier's prediction uncertain if they fall within a margin (e.g. in \\[0.45,0.55\\] for binary classifier probabilities) (similar to [Sethi and Kantardzic (2017)](https://arxiv.org/abs/1704.00023))."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "cd = ClassifierUncertaintyDrift(\n",
    "  X_ref, model=clf, backend='tensorflow', p_val=0.05, preds_type='probs'\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's check whether the detector thinks drift occurred on the different test sets and time the prediction calls:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from timeit import default_timer as timer\n",
    "\n",
    "labels = ['No!', 'Yes!']\n",
    "\n",
    "def make_predictions(cd, x_h0, x_corr, corruption):\n",
    "    t = timer()\n",
    "    preds = cd.predict(x_h0)\n",
    "    dt = timer() - t\n",
    "    print('No corruption')\n",
    "    print('Drift? {}'.format(labels[preds['data']['is_drift']]))\n",
    "    print('Feature-wise p-values:')\n",
    "    print(preds['data']['p_val'])\n",
    "    print(f'Time (s) {dt:.3f}')\n",
    "    \n",
    "    if isinstance(x_corr, list):\n",
    "        for x, c in zip(x_corr, corruption):\n",
    "            t = timer()\n",
    "            preds = cd.predict(x)\n",
    "            dt = timer() - t\n",
    "            print('')\n",
    "            print(f'Corruption type: {c}')\n",
    "            print('Drift? {}'.format(labels[preds['data']['is_drift']]))\n",
    "            print('Feature-wise p-values:')\n",
    "            print(preds['data']['p_val'])\n",
    "            print(f'Time (s) {dt:.3f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No corruption\n",
      "Drift? No!\n",
      "Feature-wise p-values:\n",
      "[0.7868902]\n",
      "Time (s) 15.574\n",
      "\n",
      "Corruption type: gaussian_noise\n",
      "Drift? Yes!\n",
      "Feature-wise p-values:\n",
      "[0.]\n",
      "Time (s) 33.066\n",
      "\n",
      "Corruption type: motion_blur\n",
      "Drift? Yes!\n",
      "Feature-wise p-values:\n",
      "[0.]\n",
      "Time (s) 32.637\n",
      "\n",
      "Corruption type: brightness\n",
      "Drift? No!\n",
      "Feature-wise p-values:\n",
      "[0.1102559]\n",
      "Time (s) 34.126\n",
      "\n",
      "Corruption type: pixelate\n",
      "Drift? Yes!\n",
      "Feature-wise p-values:\n",
      "[0.]\n",
      "Time (s) 34.351\n"
     ]
    }
   ],
   "source": [
    "make_predictions(cd, X_h0, X_c, corruption)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note here how drift is only detected for the corrupted datasets on which the model's performance is significantly degraded. For the 'brightness' corruption, for which the model maintains 89% classification accuracy, the change in model uncertainty is not deemed significant (p-value 0.11, above the 0.05 threshold). For the other corruptions which signficiantly hamper model performance, the malicious drift is detected."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regressor uncertainty based drift detection\n",
    "\n",
    "We now demonstrate how to leverage model uncertainty to detect malicious drift when the model of interest is a regressor. This is a less general approach as regressors often make point-predictions with no associated notion of uncertainty. However, if the model makes its predictions by ensembling the predicitons of sub-models then we can consider the variation in the sub-model predictions as a notion of uncertainty. `RegressorUncertaintyDetector` facilitates models that output a vector of such sub-model predictions (`uncertainty_type='ensemble'`) or deep learning models that include dropout layers and can therefore (as noted by [Gal and Ghahramani 2016](https://arxiv.org/abs/1506.02142)) be considered as an ensemble (`uncertainty_type='mc_dropout'`, the default option).\n",
    "\n",
    "#### Dataset\n",
    "\n",
    "The [Wine Quality Data Set](https://archive.ics.uci.edu/ml/datasets/wine+quality) consists of 1599 and 4898 samples of red and white wine respectively. Each sample has an associated quality (as determined by experts) and 11 numeric features indicating its acidity, density, pH etc. We consider the regression problem of tring to predict the quality of red wine sample given these features. We will then consider whether the model remains suitable for predicting the quality of white wine samples or whether the associated change in the underlying distribution should be considered as malicious drift.\n",
    "\n",
    "First we load in the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>fixed acidity</th>\n",
       "      <th>volatile acidity</th>\n",
       "      <th>citric acid</th>\n",
       "      <th>residual sugar</th>\n",
       "      <th>chlorides</th>\n",
       "      <th>free sulfur dioxide</th>\n",
       "      <th>total sulfur dioxide</th>\n",
       "      <th>density</th>\n",
       "      <th>pH</th>\n",
       "      <th>sulphates</th>\n",
       "      <th>alcohol</th>\n",
       "      <th>quality</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1599.000000</td>\n",
       "      <td>1599.000000</td>\n",
       "      <td>1599.000000</td>\n",
       "      <td>1599.000000</td>\n",
       "      <td>1599.000000</td>\n",
       "      <td>1599.000000</td>\n",
       "      <td>1599.000000</td>\n",
       "      <td>1599.000000</td>\n",
       "      <td>1599.000000</td>\n",
       "      <td>1599.000000</td>\n",
       "      <td>1599.000000</td>\n",
       "      <td>1599.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>8.319637</td>\n",
       "      <td>0.527821</td>\n",
       "      <td>0.270976</td>\n",
       "      <td>2.538806</td>\n",
       "      <td>0.087467</td>\n",
       "      <td>15.874922</td>\n",
       "      <td>46.467792</td>\n",
       "      <td>0.996747</td>\n",
       "      <td>3.311113</td>\n",
       "      <td>0.658149</td>\n",
       "      <td>10.422983</td>\n",
       "      <td>5.636023</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1.741096</td>\n",
       "      <td>0.179060</td>\n",
       "      <td>0.194801</td>\n",
       "      <td>1.409928</td>\n",
       "      <td>0.047065</td>\n",
       "      <td>10.460157</td>\n",
       "      <td>32.895324</td>\n",
       "      <td>0.001887</td>\n",
       "      <td>0.154386</td>\n",
       "      <td>0.169507</td>\n",
       "      <td>1.065668</td>\n",
       "      <td>0.807569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>4.600000</td>\n",
       "      <td>0.120000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.900000</td>\n",
       "      <td>0.012000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>0.990070</td>\n",
       "      <td>2.740000</td>\n",
       "      <td>0.330000</td>\n",
       "      <td>8.400000</td>\n",
       "      <td>3.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>7.100000</td>\n",
       "      <td>0.390000</td>\n",
       "      <td>0.090000</td>\n",
       "      <td>1.900000</td>\n",
       "      <td>0.070000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>22.000000</td>\n",
       "      <td>0.995600</td>\n",
       "      <td>3.210000</td>\n",
       "      <td>0.550000</td>\n",
       "      <td>9.500000</td>\n",
       "      <td>5.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>7.900000</td>\n",
       "      <td>0.520000</td>\n",
       "      <td>0.260000</td>\n",
       "      <td>2.200000</td>\n",
       "      <td>0.079000</td>\n",
       "      <td>14.000000</td>\n",
       "      <td>38.000000</td>\n",
       "      <td>0.996750</td>\n",
       "      <td>3.310000</td>\n",
       "      <td>0.620000</td>\n",
       "      <td>10.200000</td>\n",
       "      <td>6.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>9.200000</td>\n",
       "      <td>0.640000</td>\n",
       "      <td>0.420000</td>\n",
       "      <td>2.600000</td>\n",
       "      <td>0.090000</td>\n",
       "      <td>21.000000</td>\n",
       "      <td>62.000000</td>\n",
       "      <td>0.997835</td>\n",
       "      <td>3.400000</td>\n",
       "      <td>0.730000</td>\n",
       "      <td>11.100000</td>\n",
       "      <td>6.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>15.900000</td>\n",
       "      <td>1.580000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>15.500000</td>\n",
       "      <td>0.611000</td>\n",
       "      <td>72.000000</td>\n",
       "      <td>289.000000</td>\n",
       "      <td>1.003690</td>\n",
       "      <td>4.010000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>14.900000</td>\n",
       "      <td>8.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "       fixed acidity  volatile acidity  citric acid  residual sugar  \\\n",
       "count    1599.000000       1599.000000  1599.000000     1599.000000   \n",
       "mean        8.319637          0.527821     0.270976        2.538806   \n",
       "std         1.741096          0.179060     0.194801        1.409928   \n",
       "min         4.600000          0.120000     0.000000        0.900000   \n",
       "25%         7.100000          0.390000     0.090000        1.900000   \n",
       "50%         7.900000          0.520000     0.260000        2.200000   \n",
       "75%         9.200000          0.640000     0.420000        2.600000   \n",
       "max        15.900000          1.580000     1.000000       15.500000   \n",
       "\n",
       "         chlorides  free sulfur dioxide  total sulfur dioxide      density  \\\n",
       "count  1599.000000          1599.000000           1599.000000  1599.000000   \n",
       "mean      0.087467            15.874922             46.467792     0.996747   \n",
       "std       0.047065            10.460157             32.895324     0.001887   \n",
       "min       0.012000             1.000000              6.000000     0.990070   \n",
       "25%       0.070000             7.000000             22.000000     0.995600   \n",
       "50%       0.079000            14.000000             38.000000     0.996750   \n",
       "75%       0.090000            21.000000             62.000000     0.997835   \n",
       "max       0.611000            72.000000            289.000000     1.003690   \n",
       "\n",
       "                pH    sulphates      alcohol      quality  \n",
       "count  1599.000000  1599.000000  1599.000000  1599.000000  \n",
       "mean      3.311113     0.658149    10.422983     5.636023  \n",
       "std       0.154386     0.169507     1.065668     0.807569  \n",
       "min       2.740000     0.330000     8.400000     3.000000  \n",
       "25%       3.210000     0.550000     9.500000     5.000000  \n",
       "50%       3.310000     0.620000    10.200000     6.000000  \n",
       "75%       3.400000     0.730000    11.100000     6.000000  \n",
       "max       4.010000     2.000000    14.900000     8.000000  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "red = pd.read_csv(\n",
    "    \"http://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-red.csv\", sep=';'\n",
    ")\n",
    "white = pd.read_csv(\n",
    "    \"http://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv\", sep=';'\n",
    ")\n",
    "red.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the data for both red and white wine samples take the same format."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>fixed acidity</th>\n",
       "      <th>volatile acidity</th>\n",
       "      <th>citric acid</th>\n",
       "      <th>residual sugar</th>\n",
       "      <th>chlorides</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>4898.000000</td>\n",
       "      <td>4898.000000</td>\n",
       "      <td>4898.000000</td>\n",
       "      <td>4898.000000</td>\n",
       "      <td>4898.000000</td>\n",
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       "      <td>4898.000000</td>\n",
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       "      <th>mean</th>\n",
       "      <td>6.854788</td>\n",
       "      <td>0.278241</td>\n",
       "      <td>0.334192</td>\n",
       "      <td>6.391415</td>\n",
       "      <td>0.045772</td>\n",
       "      <td>35.308085</td>\n",
       "      <td>138.360657</td>\n",
       "      <td>0.994027</td>\n",
       "      <td>3.188267</td>\n",
       "      <td>0.489847</td>\n",
       "      <td>10.514267</td>\n",
       "      <td>5.877909</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.843868</td>\n",
       "      <td>0.100795</td>\n",
       "      <td>0.121020</td>\n",
       "      <td>5.072058</td>\n",
       "      <td>0.021848</td>\n",
       "      <td>17.007137</td>\n",
       "      <td>42.498065</td>\n",
       "      <td>0.002991</td>\n",
       "      <td>0.151001</td>\n",
       "      <td>0.114126</td>\n",
       "      <td>1.230621</td>\n",
       "      <td>0.885639</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>3.800000</td>\n",
       "      <td>0.080000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.600000</td>\n",
       "      <td>0.009000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>0.987110</td>\n",
       "      <td>2.720000</td>\n",
       "      <td>0.220000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>3.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>6.300000</td>\n",
       "      <td>0.210000</td>\n",
       "      <td>0.270000</td>\n",
       "      <td>1.700000</td>\n",
       "      <td>0.036000</td>\n",
       "      <td>23.000000</td>\n",
       "      <td>108.000000</td>\n",
       "      <td>0.991723</td>\n",
       "      <td>3.090000</td>\n",
       "      <td>0.410000</td>\n",
       "      <td>9.500000</td>\n",
       "      <td>5.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>6.800000</td>\n",
       "      <td>0.260000</td>\n",
       "      <td>0.320000</td>\n",
       "      <td>5.200000</td>\n",
       "      <td>0.043000</td>\n",
       "      <td>34.000000</td>\n",
       "      <td>134.000000</td>\n",
       "      <td>0.993740</td>\n",
       "      <td>3.180000</td>\n",
       "      <td>0.470000</td>\n",
       "      <td>10.400000</td>\n",
       "      <td>6.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>7.300000</td>\n",
       "      <td>0.320000</td>\n",
       "      <td>0.390000</td>\n",
       "      <td>9.900000</td>\n",
       "      <td>0.050000</td>\n",
       "      <td>46.000000</td>\n",
       "      <td>167.000000</td>\n",
       "      <td>0.996100</td>\n",
       "      <td>3.280000</td>\n",
       "      <td>0.550000</td>\n",
       "      <td>11.400000</td>\n",
       "      <td>6.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>14.200000</td>\n",
       "      <td>1.100000</td>\n",
       "      <td>1.660000</td>\n",
       "      <td>65.800000</td>\n",
       "      <td>0.346000</td>\n",
       "      <td>289.000000</td>\n",
       "      <td>440.000000</td>\n",
       "      <td>1.038980</td>\n",
       "      <td>3.820000</td>\n",
       "      <td>1.080000</td>\n",
       "      <td>14.200000</td>\n",
       "      <td>9.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       fixed acidity  volatile acidity  citric acid  residual sugar  \\\n",
       "count    4898.000000       4898.000000  4898.000000     4898.000000   \n",
       "mean        6.854788          0.278241     0.334192        6.391415   \n",
       "std         0.843868          0.100795     0.121020        5.072058   \n",
       "min         3.800000          0.080000     0.000000        0.600000   \n",
       "25%         6.300000          0.210000     0.270000        1.700000   \n",
       "50%         6.800000          0.260000     0.320000        5.200000   \n",
       "75%         7.300000          0.320000     0.390000        9.900000   \n",
       "max        14.200000          1.100000     1.660000       65.800000   \n",
       "\n",
       "         chlorides  free sulfur dioxide  total sulfur dioxide      density  \\\n",
       "count  4898.000000          4898.000000           4898.000000  4898.000000   \n",
       "mean      0.045772            35.308085            138.360657     0.994027   \n",
       "std       0.021848            17.007137             42.498065     0.002991   \n",
       "min       0.009000             2.000000              9.000000     0.987110   \n",
       "25%       0.036000            23.000000            108.000000     0.991723   \n",
       "50%       0.043000            34.000000            134.000000     0.993740   \n",
       "75%       0.050000            46.000000            167.000000     0.996100   \n",
       "max       0.346000           289.000000            440.000000     1.038980   \n",
       "\n",
       "                pH    sulphates      alcohol      quality  \n",
       "count  4898.000000  4898.000000  4898.000000  4898.000000  \n",
       "mean      3.188267     0.489847    10.514267     5.877909  \n",
       "std       0.151001     0.114126     1.230621     0.885639  \n",
       "min       2.720000     0.220000     8.000000     3.000000  \n",
       "25%       3.090000     0.410000     9.500000     5.000000  \n",
       "50%       3.180000     0.470000    10.400000     6.000000  \n",
       "75%       3.280000     0.550000    11.400000     6.000000  \n",
       "max       3.820000     1.080000    14.200000     9.000000  "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "white.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We shuffle and normalise the data such that each feature takes a value in \\[0,1\\], as does the quality we seek to predict."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "red, white = np.asarray(red, np.float32), np.asarray(white, np.float32)\n",
    "n_red, n_white = red.shape[0], white.shape[0]\n",
    "\n",
    "col_maxes = red.max(axis=0)\n",
    "red, white = red / col_maxes, white / col_maxes\n",
    "red, white = red[np.random.permutation(n_red)], white[np.random.permutation(n_white)]\n",
    "X, y = red[:, :-1], red[:, -1:]\n",
    "X_corr, y_corr = white[:, :-1], white[:, -1:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We split the red wine data into a set on which to train the model, a reference set with which to instantiate the detector and a set which the detector should not flag drift. We then instantiate a DataLoader to pass the training data to a PyTorch model in batches."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, y_train = X[:(n_red//2)], y[:(n_red//2)]\n",
    "X_ref, y_ref = X[(n_red//2):(3*n_red//4)], y[(n_red//2):(3*n_red//4)]\n",
    "X_h0, y_h0 = X[(3*n_red//4):], y[(3*n_red//4):]\n",
    "\n",
    "X_train_ds = torch.utils.data.TensorDataset(torch.tensor(X_train), torch.tensor(y_train))\n",
    "X_train_dl = torch.utils.data.DataLoader(X_train_ds, batch_size=32, shuffle=True, drop_last=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Regression model\n",
    "\n",
    "We now define the regression model that we'll train to predict the quality from the features. The exact details aren't important other than the presence of at least one dropout layer. We then train the model for 20 epochs to optimise the mean square error on the training data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/oliver/Projects/alibi-detect/.venv/lib/python3.8/site-packages/torch/cuda/__init__.py:52: UserWarning: CUDA initialization: Found no NVIDIA driver on your system. Please check that you have an NVIDIA GPU and installed a driver from http://www.nvidia.com/Download/index.aspx (Triggered internally at  /pytorch/c10/cuda/CUDAFunctions.cpp:100.)\n",
      "  return torch._C._cuda_getDeviceCount() > 0\n",
      "Epoch 1/30: 100%|██████████| 24/24 [00:00<00:00, 267.60it/s, loss=0.119]\n",
      "Epoch 2/30: 100%|██████████| 24/24 [00:00<00:00, 267.14it/s, loss=0.0857]\n",
      "Epoch 3/30: 100%|██████████| 24/24 [00:00<00:00, 266.90it/s, loss=0.043]\n",
      "Epoch 4/30: 100%|██████████| 24/24 [00:00<00:00, 250.43it/s, loss=0.0553]\n",
      "Epoch 5/30: 100%|██████████| 24/24 [00:00<00:00, 187.70it/s, loss=0.0365]\n",
      "Epoch 6/30: 100%|██████████| 24/24 [00:00<00:00, 260.13it/s, loss=0.03]\n",
      "Epoch 7/30: 100%|██████████| 24/24 [00:00<00:00, 245.26it/s, loss=0.0552]\n",
      "Epoch 8/30: 100%|██████████| 24/24 [00:00<00:00, 241.64it/s, loss=0.0335]\n",
      "Epoch 9/30: 100%|██████████| 24/24 [00:00<00:00, 229.60it/s, loss=0.0254]\n",
      "Epoch 10/30: 100%|██████████| 24/24 [00:00<00:00, 244.06it/s, loss=0.0223]\n",
      "Epoch 11/30: 100%|██████████| 24/24 [00:00<00:00, 225.92it/s, loss=0.0224]\n",
      "Epoch 12/30: 100%|██████████| 24/24 [00:00<00:00, 204.65it/s, loss=0.0254]\n",
      "Epoch 13/30: 100%|██████████| 24/24 [00:00<00:00, 226.55it/s, loss=0.0236]\n",
      "Epoch 14/30: 100%|██████████| 24/24 [00:00<00:00, 226.15it/s, loss=0.0247]\n",
      "Epoch 15/30: 100%|██████████| 24/24 [00:00<00:00, 250.90it/s, loss=0.0292]\n",
      "Epoch 16/30: 100%|██████████| 24/24 [00:00<00:00, 208.73it/s, loss=0.0263]\n",
      "Epoch 17/30: 100%|██████████| 24/24 [00:00<00:00, 294.98it/s, loss=0.0163]\n",
      "Epoch 18/30: 100%|██████████| 24/24 [00:00<00:00, 173.03it/s, loss=0.0223]\n",
      "Epoch 19/30: 100%|██████████| 24/24 [00:00<00:00, 186.12it/s, loss=0.0244]\n",
      "Epoch 20/30: 100%|██████████| 24/24 [00:00<00:00, 228.75it/s, loss=0.0295]\n",
      "Epoch 21/30: 100%|██████████| 24/24 [00:00<00:00, 240.64it/s, loss=0.0218]\n",
      "Epoch 22/30: 100%|██████████| 24/24 [00:00<00:00, 242.33it/s, loss=0.019]\n",
      "Epoch 23/30: 100%|██████████| 24/24 [00:00<00:00, 275.11it/s, loss=0.0257]\n",
      "Epoch 24/30: 100%|██████████| 24/24 [00:00<00:00, 267.61it/s, loss=0.0165]\n",
      "Epoch 25/30: 100%|██████████| 24/24 [00:00<00:00, 290.65it/s, loss=0.0192]\n",
      "Epoch 26/30: 100%|██████████| 24/24 [00:00<00:00, 259.52it/s, loss=0.0224]\n",
      "Epoch 27/30: 100%|██████████| 24/24 [00:00<00:00, 244.17it/s, loss=0.0173]\n",
      "Epoch 28/30: 100%|██████████| 24/24 [00:00<00:00, 261.72it/s, loss=0.0159]\n",
      "Epoch 29/30: 100%|██████████| 24/24 [00:00<00:00, 293.25it/s, loss=0.012]\n",
      "Epoch 30/30: 100%|██████████| 24/24 [00:00<00:00, 298.45it/s, loss=0.022]\n"
     ]
    }
   ],
   "source": [
    "reg = nn.Sequential(\n",
    "    nn.Linear(11, 16),\n",
    "    nn.ReLU(),\n",
    "    nn.Dropout(0.5),\n",
    "    nn.Linear(16, 32),\n",
    "    nn.ReLU(),\n",
    "    nn.Dropout(0.5),\n",
    "    nn.Linear(32, 1)\n",
    ")\n",
    "device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')\n",
    "trainer(reg, nn.MSELoss(), X_train_dl, device, torch.optim.Adam, learning_rate=0.001, epochs=30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now evaluate the trained model on both unseen samples of red wine and white wine. We see that, unsurprisingly, the model is better able to predict the quality of unseen red wine samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE when predicting the quality of unseen red wine samples: 0.008570569567382336\n",
      "MSE when predicting the quality of unseen white wine samples: 0.014613097533583641\n"
     ]
    }
   ],
   "source": [
    "reg = reg.eval()\n",
    "reg_fn = encompass_batching(reg, backend='pytorch', batch_size=32)\n",
    "preds_ref = reg_fn(X_ref)\n",
    "preds_corr = reg_fn(X_corr)\n",
    "\n",
    "ref_mse = np.square(preds_ref - y_ref).mean()\n",
    "corr_mse = np.square(preds_corr - y_corr).mean()\n",
    "\n",
    "print(f'MSE when predicting the quality of unseen red wine samples: {ref_mse}')\n",
    "print(f'MSE when predicting the quality of unseen white wine samples: {corr_mse}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Detect drift\n",
    "\n",
    "We now look at whether a regressor-uncertainty detector would have picked up on this malicious drift. We instantiate the detector and obtain drift predictions on both the held-out red-wine samples and the white-wine samples. We specify `uncertainty_type='mc_dropout'` in this case, but alternatively we could have trained an ensemble model that for each instance outputs a vector of multiple independent predictions and specified `uncertainty_type='ensemble'`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Drift detected on unseen red wine samples? no\n",
      "Drift detected on white wine samples? yes\n",
      "p-value on unseen red wine samples? [0.23237702]\n",
      "p-value on white wine samples? [1.7934791e-10]\n"
     ]
    }
   ],
   "source": [
    "cd = RegressorUncertaintyDrift(\n",
    "    X_ref, model=reg, backend='pytorch', p_val=0.05, uncertainty_type='mc_dropout', n_evals=100\n",
    ")\n",
    "preds_h0 = cd.predict(X_h0)\n",
    "preds_h1 = cd.predict(X_corr)\n",
    "\n",
    "print(f\"Drift detected on unseen red wine samples? {'yes' if preds_h0['data']['is_drift']==1 else 'no'}\")\n",
    "print(f\"Drift detected on white wine samples? {'yes' if preds_h1['data']['is_drift']==1 else 'no'}\")\n",
    "\n",
    "print(f\"p-value on unseen red wine samples? {preds_h0['data']['p_val']}\")\n",
    "print(f\"p-value on white wine samples? {preds_h1['data']['p_val']}\")"
   ]
  }
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