JEM.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Replicating the paper \"Your Classifier is Secretely an Energy Based Model and you should treat it like one\"\n",
    "\n",
    "Here, I attempt to replicate the paper in the title, by Grathwohl et al."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "import tensorflow.keras as keras\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "from sgld_sampler import sgld_sample\n",
    "from JEM import JEM\n",
    "from scores import inception_score, frechet_inception_distance\n",
    "from wrn import create_wide_residual_network"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Classifier for IS/FID\n",
    "\n",
    "For using IS/FID, we need a classifier. Therefore, we quickly train a classifier for CIFAR-10. We reuse the one from the EBM experiment."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Loading the training data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((60000, 28, 28), (60000,))"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(X_train_full, y_train_full), (X_test, y_test) = keras.datasets.mnist.load_data()\n",
    "X_train_full = X_train_full / 255.0\n",
    "X_test = X_test / 255.0\n",
    "X_train_full.shape, y_train_full.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_valid, X_train = X_train_full[:5000], X_train_full[5000:]\n",
    "y_valid, y_train = y_train_full[:5000], y_train_full[5000:]\n",
    "\n",
    "def vgg_block(layer_in, n_filters, n_conv):\n",
    "    # Add convolutional layers\n",
    "    for _ in range(n_conv):\n",
    "        layer_in = keras.layers.Conv2D(n_filters, (3,3), padding='same', activation='relu')(layer_in)\n",
    "    # Add max pooling layer\n",
    "    layer_in = keras.layers.MaxPooling2D((2,2), strides=(2,2))(layer_in)\n",
    "    return layer_in\n",
    "\n",
    "input_ = keras.layers.Input(shape=(28, 28, 1))\n",
    "vgg_1 = vgg_block(input_, 128, 3) # 14, 14, 128\n",
    "vgg_2 = vgg_block(vgg_1, 256, 3) # 7, 7, 256\n",
    "flatten = keras.layers.Flatten()(vgg_2)\n",
    "output = keras.layers.Dense(10, activation='softmax')(flatten)\n",
    "model = keras.Model(inputs=input_, outputs=output)\n",
    "model.summary()\n",
    "\n",
    "model.compile(loss=\"sparse_categorical_crossentropy\",\n",
    "              optimizer=\"sgd\", metrics=[\"accuracy\"])\n",
    "early_stopping = keras.callbacks.EarlyStopping(patience=5, \n",
    "                                               restore_best_weights=True)\n",
    "history = model.fit(X_train, y_train, epochs=5,\n",
    "                    validation_data=(X_valid, y_valid),\n",
    "                    callbacks=[early_stopping])\n",
    "mnist_classifier = keras.models.load_model('mnist-classifier-1')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use this classifier for our experiments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "mnist_classifier = keras.models.load_model('mnist-classifier-1')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## JEM network\n",
    "\n",
    "I use a wide ResNet with no stochastic regularization, as done in the paper."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"model_2\"\n",
      "__________________________________________________________________________________________________\n",
      "Layer (type)                    Output Shape         Param #     Connected to                     \n",
      "==================================================================================================\n",
      "input_2 (InputLayer)            [(None, 28, 28, 1)]  0                                            \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_19 (Conv2D)              (None, 28, 28, 16)   144         input_2[0][0]                    \n",
      "__________________________________________________________________________________________________\n",
      "activation_17 (Activation)      (None, 28, 28, 16)   0           conv2d_19[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_20 (Conv2D)              (None, 28, 28, 64)   9216        activation_17[0][0]              \n",
      "__________________________________________________________________________________________________\n",
      "activation_18 (Activation)      (None, 28, 28, 64)   0           conv2d_20[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_21 (Conv2D)              (None, 28, 28, 64)   36864       activation_18[0][0]              \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_22 (Conv2D)              (None, 28, 28, 64)   1024        activation_17[0][0]              \n",
      "__________________________________________________________________________________________________\n",
      "add_8 (Add)                     (None, 28, 28, 64)   0           conv2d_21[0][0]                  \n",
      "                                                                 conv2d_22[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "activation_19 (Activation)      (None, 28, 28, 64)   0           add_8[0][0]                      \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_23 (Conv2D)              (None, 28, 28, 64)   36864       activation_19[0][0]              \n",
      "__________________________________________________________________________________________________\n",
      "activation_20 (Activation)      (None, 28, 28, 64)   0           conv2d_23[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_24 (Conv2D)              (None, 28, 28, 64)   36864       activation_20[0][0]              \n",
      "__________________________________________________________________________________________________\n",
      "add_9 (Add)                     (None, 28, 28, 64)   0           add_8[0][0]                      \n",
      "                                                                 conv2d_24[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "activation_21 (Activation)      (None, 28, 28, 64)   0           add_9[0][0]                      \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_25 (Conv2D)              (None, 14, 14, 128)  73728       activation_21[0][0]              \n",
      "__________________________________________________________________________________________________\n",
      "activation_22 (Activation)      (None, 14, 14, 128)  0           conv2d_25[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_26 (Conv2D)              (None, 14, 14, 128)  147456      activation_22[0][0]              \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_27 (Conv2D)              (None, 14, 14, 128)  8192        activation_21[0][0]              \n",
      "__________________________________________________________________________________________________\n",
      "add_10 (Add)                    (None, 14, 14, 128)  0           conv2d_26[0][0]                  \n",
      "                                                                 conv2d_27[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "activation_23 (Activation)      (None, 14, 14, 128)  0           add_10[0][0]                     \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_28 (Conv2D)              (None, 14, 14, 128)  147456      activation_23[0][0]              \n",
      "__________________________________________________________________________________________________\n",
      "activation_24 (Activation)      (None, 14, 14, 128)  0           conv2d_28[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_29 (Conv2D)              (None, 14, 14, 128)  147456      activation_24[0][0]              \n",
      "__________________________________________________________________________________________________\n",
      "add_11 (Add)                    (None, 14, 14, 128)  0           add_10[0][0]                     \n",
      "                                                                 conv2d_29[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "activation_25 (Activation)      (None, 14, 14, 128)  0           add_11[0][0]                     \n",
      "__________________________________________________________________________________________________\n",
      "average_pooling2d_1 (AveragePoo (None, 1, 1, 128)    0           activation_25[0][0]              \n",
      "__________________________________________________________________________________________________\n",
      "flatten_1 (Flatten)             (None, 128)          0           average_pooling2d_1[0][0]        \n",
      "__________________________________________________________________________________________________\n",
      "dense_1 (Dense)                 (None, 10)           1290        flatten_1[0][0]                  \n",
      "==================================================================================================\n",
      "Total params: 646,554\n",
      "Trainable params: 646,554\n",
      "Non-trainable params: 0\n",
      "__________________________________________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "ebm_model = create_wide_residual_network((28, 28, 1), nb_classes=10, N=2, k=4)\n",
    "ebm_model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluation of network performance\n",
    "\n",
    "To evaluate the network performance, I use metrics, like the IS and FID. The way these are evaluated is that at every batch, they are applied to the generated and real samples. The metrics are then stored in a list. At the end of an epoch, I look at the mean value for each metric of the current epoch and at the last epoch. If the mean value of the current epoch is higher than the mean value of the last epoch, I conclude that the network learned something and save the weights. If not, I conclude that the network has converged or overfit and stop the learning process. For multiple metrics, I perform a majority vote: If the majority agrees that learning occured, I continue. If not, I stop the learning process.\n",
    "\n",
    "At the end of the learning process, the ```EBM``` object records the trend for all metrics and the best values achieved. Note that I assume that for all metrics, it holds that a higher value means a better value; therefore I negate the FID to fit in that framework. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fuse_images(width, height, images, img_width, img_height):\n",
    "    really_big_image = None\n",
    "    for i in range(width):\n",
    "        big_image = None\n",
    "        for j in range(height):\n",
    "            cur_image = images[width * i + j].reshape(img_width, img_height)\n",
    "            if big_image is not None:\n",
    "                big_image = np.hstack((big_image, cur_image))\n",
    "            else:\n",
    "                big_image = cur_image\n",
    "        if really_big_image is not None:\n",
    "            really_big_image = np.vstack((really_big_image, big_image))\n",
    "        else:\n",
    "            really_big_image = big_image\n",
    "    return really_big_image\n",
    "\n",
    "def is_metric_callback(samples_data, samples_energ, it):\n",
    "    p_yx = mnist_classifier(samples_energ).numpy()\n",
    "    score = inception_score(p_yx)\n",
    "    return score\n",
    "\n",
    "# Need last-layer activations for FID\n",
    "mnist_statistics = keras.Model(mnist_classifier.input, mnist_classifier.get_layer(name='flatten').output)\n",
    "\n",
    "def fid_metric_callback(samples_data, samples_energ, it):\n",
    "    stats_gen = mnist_statistics(samples_energ)\n",
    "    stats_real = mnist_statistics(samples_data)\n",
    "    score = frechet_inception_distance(stats_real, stats_gen)\n",
    "    return -score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "optimizer = keras.optimizers.Adam(1e-4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "jem = JEM(ebm_model, optimizer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "history = jem.fit(X_train_full, y_train_full, 128, 25, optimizer, 0.0, 1.0, num_steps_markov=tf.constant(120),\n",
    "        var=tf.constant(1e-2 ** 2), step_size=tf.constant(2.0), callbacks_energy=[],\n",
    "        metrics_samples=[(\"IS\", is_metric_callback), (\"FID\", fid_metric_callback)],\n",
    "        alpha=tf.constant(0.0), clip_thresh=tf.constant(1e6),\n",
    "        weight_ce_loss=tf.constant(1.0), save_best_weights=True, use_replay_buffer=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "batch_size = 10\n",
    "x_init = tf.random.uniform(shape=(batch_size, 28, 28))\n",
    "imgs = sgld_sample(jem.energy, x_init, tf.constant(1000), 1, 0.001 ** 2, clip_thresh=tf.constant(1.0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x1080 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "imgs = np.clip(imgs, 0, 1)\n",
    "img = fuse_images(3, 3, imgs, 28, 28)\n",
    "plt.figure(figsize=(15, 15))\n",
    "plt.imshow(img)\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test set accuracy of the JEM model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "preds_test = jem.classify(X_train_full)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_test_one_hot = tf.keras.backend.one_hot(y_test, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "m = tf.keras.metrics.categorical_accuracy(y_test_one_hot, preds_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9572"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(m.numpy())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calibration of the classifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "pred_confidence = np.max(preds_test, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.4682794 , 0.9580364 , 0.9531985 , ..., 0.83769923, 0.8182639 ,\n",
       "       0.6720254 ], dtype=float32)"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred_confidence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_thresholds(X, y, performance, thresholds):\n",
    "    sets = []\n",
    "    initial = 0.0\n",
    "    for threshold in thresholds:\n",
    "        indices = np.logical_and(performance > initial, performance < threshold)\n",
    "        sets.append((X[indices], y[indices]))\n",
    "        initial = threshold\n",
    "    return sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [],
   "source": [
    "perf_buckets = make_thresholds(X_train_full, y_train_full, pred_confidence, [0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train = tf.keras.backend.one_hot(y_train_full, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [],
   "source": [
    "conf_avg = []\n",
    "for data, labels in perf_buckets:\n",
    "    preds = jem.classify(data)\n",
    "    y = tf.keras.backend.one_hot(labels, 10)\n",
    "    m = tf.keras.metrics.categorical_accuracy(y, preds)\n",
    "    conf_avg.append(np.mean(m.numpy()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.4,\n",
       " 0.3619403,\n",
       " 0.53481483,\n",
       " 0.6829828,\n",
       " 0.83304894,\n",
       " 0.93706435,\n",
       " 0.9797178,\n",
       " 0.9947166]"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "conf_avg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "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": [
    "plt.bar([0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9], conf_avg, width=0.05)\n",
    "plt.plot(np.linspace(0.2, 0.9, 100),np.linspace(0.2, 0.9, 100), c=\"red\", label=\"Ideal trend\")\n",
    "plt.ylabel(\"Model performance\")\n",
    "plt.xlabel(\"Model confidence\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Out-of-distribution detection - using FashionMNIST"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using likelihood"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((60000, 28, 28), (60000,))"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(X_train_full_fm, y_train_full_fm), (X_test_fm, y_test_fm) = tf.keras.datasets.fashion_mnist.load_data()\n",
    "X_train_full_fm = X_train_full_fm / 255.0\n",
    "X_test_fm = X_test_fm / 255.0\n",
    "X_train_full_fm.shape, y_train_full_fm.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 312,
   "metadata": {},
   "outputs": [],
   "source": [
    "energs_fm = jem.get_likelihoods(X_train_full_fm)\n",
    "energs_mnist = jem.get_likelihoods(X_train_full)\n",
    "energ_min_mnist = np.min(-energs_mnist)\n",
    "energ_min_fm = np.min(-energs_fm)\n",
    "energ_max_mnist = np.max(-energs_mnist)\n",
    "energ_max_fm = np.max(-energs_fm)\n",
    "\n",
    "energ_min = np.minimum(energ_min_mnist, energ_min_fm)\n",
    "energ_max = np.maximum(energ_max_mnist, energ_max_fm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 314,
   "metadata": {},
   "outputs": [],
   "source": [
    "energs_mnist_norm = (-energs_mnist - energ_min) / (energ_max - energ_min)\n",
    "energs_fm_norm = (-energs_fm - energ_min) / (energ_max - energ_min)\n",
    "combined_energs = np.hstack((energs_mnist_norm, energs_fm_norm))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 320,
   "metadata": {},
   "outputs": [],
   "source": [
    "labels_true = np.ones(energs_mnist_norm.shape[0])\n",
    "labels_false = np.zeros(energs_fm_norm.shape[0])\n",
    "labels = np.hstack((labels_true, labels_false))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 321,
   "metadata": {},
   "outputs": [],
   "source": [
    "aucroc = sklearn.metrics.roc_auc_score(labels, combined_energs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 322,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9738398326388888"
      ]
     },
     "execution_count": 322,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aucroc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 323,
   "metadata": {},
   "outputs": [],
   "source": [
    "fpr, tpr, thresholds = sklearn.metrics.roc_curve(labels, combined_energs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 324,
   "metadata": {},
   "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": [
    "plt.figure()\n",
    "lw = 2\n",
    "plt.plot(fpr, tpr, color='darkorange',\n",
    "         lw=lw, label='ROC curve (area = %0.2f)' % aucroc)\n",
    "plt.plot([0, 1], [0, 1], color='navy', lw=lw, linestyle='--')\n",
    "plt.xlim([-0.01, 1.0])\n",
    "plt.ylim([0.0, 1.05])\n",
    "plt.xlabel('False Positive Rate')\n",
    "plt.ylabel('True Positive Rate')\n",
    "plt.title('Receiver operating characteristic')\n",
    "plt.legend(loc=\"lower right\")\n",
    "plt.savefig(\"ROC-MNIST-L\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using Gradient Magnitude"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 332,
   "metadata": {},
   "outputs": [],
   "source": [
    "energs_fm = jem.get_energ_gradient_magnitudes(X_train_full_fm)\n",
    "energs_mnist = jem.get_energ_gradient_magnitudes(X_train_full)\n",
    "energ_min_mnist = np.min(-energs_mnist)\n",
    "energ_min_fm = np.min(-energs_fm)\n",
    "energ_max_mnist = np.max(-energs_mnist)\n",
    "energ_max_fm = np.max(-energs_fm)\n",
    "\n",
    "energ_min = np.minimum(energ_min_mnist, energ_min_fm)\n",
    "energ_max = np.maximum(energ_max_mnist, energ_max_fm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 335,
   "metadata": {},
   "outputs": [],
   "source": [
    "energs_fm_norm = (-energs_fm - energ_min) / (energ_max - energ_min)\n",
    "energs_mnist_norm = (-energs_mnist - energ_min) / (energ_max - energ_min)\n",
    "combined_energs = np.hstack((energs_mnist_norm, energs_fm_norm))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 336,
   "metadata": {},
   "outputs": [],
   "source": [
    "labels_true = np.ones(energs_mnist_norm.shape[0])\n",
    "labels_false = np.zeros(energs_fm_norm.shape[0])\n",
    "labels = np.hstack((labels_true, labels_false))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 337,
   "metadata": {},
   "outputs": [],
   "source": [
    "fpr, tpr, thresholds = sklearn.metrics.roc_curve(labels, combined_energs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 338,
   "metadata": {},
   "outputs": [],
   "source": [
    "aucroc = sklearn.metrics.roc_auc_score(labels, combined_energs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 339,
   "metadata": {},
   "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": [
    "plt.figure()\n",
    "lw = 2\n",
    "plt.plot(fpr, tpr, color='darkorange',\n",
    "         lw=lw, label='ROC curve (area = %0.2f)' % aucroc)\n",
    "plt.plot([0, 1], [0, 1], color='navy', lw=lw, linestyle='--')\n",
    "plt.xlim([-0.01, 1.0])\n",
    "plt.ylim([0.0, 1.05])\n",
    "plt.xlabel('False Positive Rate')\n",
    "plt.ylabel('True Positive Rate')\n",
    "plt.title('Receiver operating characteristic')\n",
    "plt.legend(loc=\"lower right\")\n",
    "plt.savefig(\"ROC-MNIST-G\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using Confidence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 344,
   "metadata": {},
   "outputs": [],
   "source": [
    "preds_mnist = jem.classify(X_train_full)\n",
    "pred_confidence_mnist = np.max(preds_mnist, axis=1)\n",
    "preds_fm = jem.classify(X_train_full_fm)\n",
    "pred_confidence_fm = np.max(preds_fm, axis=1)\n",
    "\n",
    "energ_min_mnist = np.min(pred_confidence_mnist)\n",
    "energ_min_fm = np.min(pred_confidence_fm)\n",
    "energ_max_mnist = np.max(pred_confidence_mnist)\n",
    "energ_max_fm = np.max(pred_confidence_fm)\n",
    "\n",
    "energ_min = np.minimum(energ_min_mnist, energ_min_fm)\n",
    "energ_max = np.maximum(energ_max_mnist, energ_max_fm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 345,
   "metadata": {},
   "outputs": [],
   "source": [
    "energs_mnist_norm = (pred_confidence_mnist - energ_min) / (energ_max - energ_min)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 346,
   "metadata": {},
   "outputs": [],
   "source": [
    "energs_fm_norm = (pred_confidence_fm - energ_min) / (energ_max - energ_min)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 347,
   "metadata": {},
   "outputs": [],
   "source": [
    "combined_energs = np.hstack((energs_mnist_norm, energs_fm_norm))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 348,
   "metadata": {},
   "outputs": [],
   "source": [
    "labels_true = np.ones(energs_mnist_norm.shape[0])\n",
    "labels_false = np.zeros(energs_fm_norm.shape[0])\n",
    "labels = np.hstack((labels_true, labels_false))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 349,
   "metadata": {},
   "outputs": [],
   "source": [
    "fpr, tpr, thresholds = sklearn.metrics.roc_curve(labels, combined_energs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 350,
   "metadata": {},
   "outputs": [],
   "source": [
    "aucroc = sklearn.metrics.roc_auc_score(labels, combined_energs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 351,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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fdfyisATb5p+41hDXyp4RxLWCuDZHmoSCQ737O1RA2707nbvv/or77judnj0bATBv3uUEBfnuYEMThQpMmXth3wrYvxoObIC9CfYMIS+j9Oljmtk+dOp0hNrtIaYp1Gxlzwg0ESgvKFms3r07nUWLbgDwaZIATRTK3xljzwz2JsC+lfZsITnR9glUmhr1oU4nqNsZarW1w/W62RvClPKRlSv3MHr0ApYu3QnA8OFtmTbtPB9HdYQmCuVfjLHNRVsWwPZvbbfOpV1VFBYDdbtC/e42IdTvCXU62CKyUlVEZmYuTzzxA5MnL6agwNC4cQxTpw7zerG6PJooVNWX8gfs+N6+dv5kL0d1FdUQGvaBBr1s01G9bhB3arXr70f5n0OHspk5M4HCQsO4cb15+ulziI0N93VYx9BEoaoWU2gLzUk/QdKPkPSDvVPZVY360PpiaH4ONDnLJooqdPSlVFn27MmgXr0aBAcH0aRJLHPmXESLFnH06dPE16EdlyYK5Xsp62HrQpsUdnx/bFNSRB1oPghOGWwTQ+32mhiU3ykoKGTWrOU89NC3PPXUQMaPt09+vvLKTj6OrHyaKJT35abDjkW2zrBrsb0yyVV0U2hyJjQ9yyaGup20GUn5tZLF6iVLkooThT/QRKG843AybP4Ytn0NWz49+r6FkBrQ9jJoOsCeOdRs4aMglapcmZm5TJy4iH/+c0lxsfrll8/jkkva+zq0E6KJQnlOfg5seh/+eBv++tI+87dIo77QYhicMgTq9zjyMBqlAsRffx1k4MDX2bYtFRG4/fY+TJo0qEoWq8ujiUJVvuRVsOrfNkFkp9jvJNgmhdYXQ8vz9axBBbzmzWtSv34UtWtHMmvWcHr3rrrF6vJoolCVIz8bNr4PidPtA++L1OsGXUdBm0vt1UlKBaiiYvVFF7WjadNYgoOD+OST/6NevShCQvy7xqaJQp2crAPw2/OwapZ9vgJAaBR0vBY632zvbdArlFSAS0y0xeply3by7bd/8cEHVwLQqFGMjyOrHJooVMUc2gIrZ8Dqfx+5nLV+D+g+Ftr/n00WSgW4ksXqJk1iuOaaLr4Oq9JpolAnJm07LP8nrHwFCnLtd80HwZnP2AK1UtXEZ59tZOzYz4uL1ePH9+Gpp/yzWF0eTRTKPelJThPTbCjIsd+1vRLi74FGfXwbm1Je9tdfBxkxYh4FBYYePRr6fbG6PJooVNmyUmDpPyBxmkuCuAL6PGDrD0pVE4WFpri775YtazFhwlnUqhXB7bf39ftidXk0UajS5aTC4idg5SzIP2y/a3MZ9HsM6nX1bWxKeVlRsXrChDMZMcLeLPfkkwN9HJX3aKJQRzMG1r8JP9wHh/fa7045F86cBA17+zY2pbysZLH6ued+4aKL2lWpLsC9QROFOiJtGyy8BbZ/Yz836gsDp2oNQlVLCxbYYvX27akEBQl33NGXp54aWO2SBGiiUAB5WbD0aVg+GfKzIKIW9H8JOl2vnfGpamf//sPcdttnvP/+OgB69mzErFnDiY9v7OPIfEcTRXW36WP4/g5I324/t70Czplmn/mgVDUUERHC0qVJREWFMmnSIMaN6xPwxeryaKKorrIOwM8P2ctdwRaoz3kFmpzh27iU8oGVK/dw6qm1iY4OIzo6jHffvYLGjWNo3rymr0OrEqp3mqyuNn4A/2lnk4QEw1nPwt9+1yShqp2MjFzuvfcrevWazWOPfV/8/WmnNdUk4ULPKKqT7IPwxbWw5TP7ufEZMHgG1Au8LgeUKk/JYrUIGGOqZbG6PJooqott38DCmyB9B4TFwBlPQ49x2mGfqnZ27kzjjju+5IMP1gNarHaHJopAV1gAi5+EJU/azw3i4cJ3oWZL38allA/s2JFKp06vkJ6eq8XqE+DRRCEiw4B/AcHAHGPMsyXG1wTeBJo7sbxojPmPJ2OqVg7vg8+vhW1f2c99J8DpT0CQHh+o6qlZs5oMGXIq+fmFTJt2Hs2aaR3CHR7bY4hIMDAdGAIkAb+JyHxjzDqXycYC64wxF4pIPWCDiLxljMn1VFzVRm46vDsQUtZBRG0Y9jqcOtzXUSnlVRkZuTz++Pdcc01XevZsBMBbb11KRIQeLJ0IT26tPsBmY8wWABGZB4wAXBOFAWLEVo+igQNAvgdjqh4ObYFPRtgkUasdXPalPnpUVTuffrqBsWM/Z8eONH75ZQeLF9+MiGiSqABPbrEmwA6Xz0lAyQcWTAPmA7uAGGCkMaaw5IJEZBQwCqB58+YeCTZgpO2AD4bCoc0Q2wIu+VSThKpWdu5MY/z4L/nwwyPF6mnTztermU6CJys4pf2rmBKfhwKJQGOgOzBNRGKPmcmY2caYeGNMfL169So7zsBxYAPMO8Mmifo94LqVUKuNr6NSyisKCgp5+eWldOgwnQ8/XE90dBhTpgxl6dJb9Iqmk+TJM4okoJnL56bYMwdXNwLPGmMMsFlE/gLaA8s8GFdgOvQnvHcOZOyEhn3g0i8g/Jicq1TA2rcvk4cf/o709Fwuvrg9U6cO02J1JfFkovgNaCMiLYGdwP8BV5eYZjtwDvCTiDQA2gFbPBhTYDq0Bd4ZYJNEo35w+UJ7r4RSAS4jI5fIyBCCg4No1CiG6dPPJyYmnIsvbu/r0AKKx5qejDH5wDhgIbAeeNcYs1ZEbhWRW53JngJOF5HVwLfAA8aY/Z6KKSClrId3zoaMJKjfEy5ZoElCVQvz52+gY8fpTJ/+W/F3117bTZOEB4ht9fEf8fHxJiEhwddhVA1pO+Dt0yBjl+2O49LPtblJBbykpDTGj/+Cjz76A4ABA1rw3XfXabG6HCKy3BgTX5F59Toxf5WVAu8NskmiUT+4/GsIjfR1VEp5TEFBIdOn/8bDD39HRkYu0dFhPP30IMaO7a1JwsM0Ufij7IPw4fn26qZ63eDSzzRJqIC2d28Gw4e/TUKCvR7mkkvaM3XqeTRtqmfQ3qCJwt9kH4J3+sP+1RDdBC6eb59Ip1QAq1u3BgBNm8Yybdp5jBihdQhv0kThT/Kz7R3X+1fbm+lGLoJYvQFRBab58zfQs2cjmjaNJTg4iHffvZy6dWsQExPu69CqHe0y0Z98fwck/WgfU3rFNxB7iq8jUqrSJSWlceml7zBixDzuuOPL4u9btqylScJH9IzCX6yYbp9IFxwGl3wGcaf6OiKlKlVpxer+/U/RhwlVAZoo/MHOX+G7cXb4nBnQsEJXuClVZf3++25Gj16gxeoqShNFVXd4HywYaYd7jIcuN/k2HqUq2Z49GfTr9yq5uQVarK6i3E4UIhJljMn0ZDCqBFMIX95o77pudBr0f8HXESlV6Ro2jObOO/uSl1fIE08M0DpEFVRuMVtETheRddhuOBCRbiLyiscjU7D6VfjrcwivCcPftfUJpfxcUbF6/vwNxd89++xgJk8eqkmiinLnjOKf2O7A5wMYY1aKyNkejUrZPpwW3WWHB0yB2GZlTq5UVVeyWL1xYwoXXtgWEdFidRXnVtOTMWZHiX/IAs+EowDIOwyfXg55mdD2Cuh0va8jUuqkLF++i9GjF7B8+W7gSLFaE4R/cCdR7BCR0wEjImHAeJxmKOUhi+52HmPaFoa+CvqfSfmpzMxcHnnkO6ZOXUZhoaFZs1imTTufiy5q5+vQ1AlwJ1HcCvwL+2jTJOArYIwng6rW1r0Bq2bZesQF/9Muw5VfMwY++MAeV95992k88cRAoqO11uZv3EkU7Ywx17h+ISJnAL94JqRqLG07fOvcL3H289Cgl2/jUaoCduxIpVatSKKjw4iODuO//72E2NhwevZs5OvQVAW504XHy25+p07Wt+MgNw1aDbf3TCjlR/LzC5kyZQkdO77CY499X/z9gAEtNEn4ueOeUYhIP+B0oJ6I3O0yKhYI9nRg1c7Wr2DLpxAaDUNmaV1C+ZXly3cxatQCfv/dFquTktIoLDQEBenfcSAoq+kpDIh2pnFtKE8DLvdkUNVOfvaRS2F73Q3RjX0bj1JuSk/P4dFHv+fll7VYHciOmyiMMT8AP4jIXGPMNi/GVP389ry9yim2BfR5wNfRKOWW5ORMevacTVJSGkFBosXqAOZOMfuwiLwAdAIiir40xgzyWFTVycHNsPQZOzz0VQit4dt4lHJTvXpR9O3bhEaNopk1azg9emgdIlC5kyjeAt4BhmMvlb0eSPZkUNXKorugIAfaXw3NNfeqqis/v5Bp05Zx9tmnFBenX331IqKjwwgO1kfbBDJ3/nXrGGNeBfKMMT8YY24CTvNwXNVD0o+wZQGERGiHf6pKW758F337zuGuuxYyatSnFBYaAGrWjNAkUQ24c0aR57zvFpELgF1AU8+FVE0U5MLXo+1w/L1awFZVUslidfPmNXn88f56NVM1406imCQiNYF7sPdPxAJ3ejKoamHFy3DgD6jZEvo86OtolDrGxx//wbhxn7NzZzrBwcK99/bj8ccHaLG6Gio3URhjFjiDqcBAKL4zW1VUbgYse9YOD5oGoVG+jUepEvbvP8x1131EenouvXs3ZvbsC+nevaGvw1I+UtYNd8HAldg+nr40xqwRkeHABCAS6OGdEANQ4nTI2g8Ne0PL83wdjVKALVaLQHBwEHXr1mDy5KFkZ+dz223xWoeo5so6o3gVaAYsA6aKyDagH/CgMeZjL8QWmLIPwZJJdrjfRL0DW1UJCQm2G/Drr+/G+PF9Abjllp4+jkpVFWUlinigqzGmUEQigP1Aa2PMHu+EFqCWvwR5GdBsILQ639fRqGouPT2HRx75jmnTfqOw0JCTk8/Ysb31DEIdpay/hlxjTCGAMSYb2KhJ4iQd+hMSXrTDpz/h21hUtffxx3/QocN0pk5dhgjce28/liy5RZOEOkZZZxTtRWSVMyzAqc5nAYwxpqvHows0P9xn+3VqNxKanuXraFQ1lZqazfXXf8wnn9hnVmuxWpWnrETRwWtRVAc7f4HNH9krnPq/6OtoVDUWHR3Gzp3pxMSE8cwz52ixWpWrrE4BtSPAylR0OWz3cRCj9ysq70pI2EWjRtE0aRJLcHAQb755CdHRYTRpEuvr0JQf8OhhhIgME5ENIrJZREq9q0xEBohIooisFZEfPBmPz+xdbrvqCI2CHrf7OhpVjaSl5XDHHV/Qt+8cxo//svj7du3qapJQbnPnzuwKce7DmA4MwT5r+zcRmW+MWecyTRzwCjDMGLNdROp7Kh6fSnjJvne5BWKa+DYWVS0YY/jooz8YP/6L4jurW7WKo6CgUJuZ1AlzK1GISCTQ3Biz4QSW3QfYbIzZ4ixjHjACWOcyzdXAh8aY7QDGmH0nsHz/kLkHNr4PEgQ97/B1NKoa2L49lXHjPufTTzcC0KdPE2bNGq7FalVh5R5aiMiFQCLwpfO5u4jMd2PZTYAdLp+TnO9ctQVqicgiEVkuIte5FbU/WT4FCvPsc7BrtvR1NCrAHTyYRdeuM/j0043ExIQxbdp5/PrrTZok1Elx54xiIvbsYBGAMSZRRFq4MV9ptxybUtbfCzgH2y3IYhFZYozZeNSCREYBowCaN2/uxqqriJw0210HaMd/yitq1Yrk5pt7sH17Gv/61zAaN44pfyalyuFOosg3xqTKiXc1kYTtAqRIU2wX5SWn2W+MyQQyReRHoBtwVKIwxswGZgPEx8eXTDZV12/P2buwm/aHxv18HY0KQGlpOTz66Hecc06r4udUP//8EK1DqErlzl/TGhG5GggWkTYi8jLwqxvz/Qa0EZGWIhIG/B9QssnqE+AsEQkRkRpAX2D9CcRfdeVlwoppdljvwlaVzBjDhx+uL76z+s47vyQ/vxBAk4SqdO78Rd2OfV52DvA/bHfjd5Y3kzEmHxgHLMTu/N81xqwVkVtF5FZnmvXY2scqbOeDc4wxayrwO6qedW9CbprtIbZZf19HowLI9u2pjBgxj8sue5ddu9Lp06cJH344kpAQTRDKM8SYsltyRKSHMWaFl+IpV3x8vElISPB1GGUrLID/doWUdXDuHOhys68jUgEgP7+QqVOX8thj35OZmUdsbDj/+Mc5jB7dS88iVLlEZLkxJr4i87pTo5gsIo2A94B5xpi1FVlRtbLhXZskoptA+6t9HY0KENnZ+UyZsoTMzDyuuKIjU6ZosVp5hztPuBsoIg2xDzGaLSKxwDvGmEkej85fFV3p1PdhCI30bSzKr6Wl5RAcLERFhREdHcarr15EXl4h55/fxtehqWrErfNVY8weY8xU4FbsPRWPeTIov3ZwE+z6xXbX0fFaX0ej/JRrsfqxx74v/n7IkFM1SSivK/eMQkQ6ACOBy4EUYB5wj4fj8l+Jr9j31pdAWLRvY1F+qeSd1UuX7iQ/v1CL1cpn3KlR/Ad4GzjXGFPyPgjlKj8b1v3XDmt3HeoElVasfvbZcxg1SovVyrfcqVGc5o1AAsLG9yD7ANTrDg0rdHGBqqbS0nLo338uiYn2IZJXXtmJKVOG0qiRFquV7x03UYjIu8aYK0VkNUd3vaFPuCuNMZA4ww53HeXbWJTfiY0N59RTa3HwYBavvHKB1iFUlVLWGUVR28lwbwTi9/78FHYvhojaWsRW5SrqBrxlyzh69GgEwMyZw4mMDCEqKszH0Sl1tOM2fBpjdjuDY4wx21xfwBjvhOdHlk+2730e0iK2KtO2bYe46CJ7Z/WoUQsoKLBdb9StW0OThKqS3KmQDSnlu/MqOxC/lvIHJP1gL4nVZid1HPn5hbz00q907PgKCxZsJDY2nJtu6k4FOtxUyqvKqlHchj1zaCUiq1xGxQC/eDowv7LSuSS27eUQro+XVMdatmwno0cv0GK18ktl1Sj+B3wB/ANwfZhCujHmgEej8ie5GbDuDTvcY7xvY1FVUnp6Duee+wapqTm0aBHHK6+cz3nnabFa+Y+yEoUxxmwVkbElR4hIbU0WjjWvQs4haNQPGvT0dTSqiijqbFNEiIkJ55lnzmHbtkM8/vgAatQI9XF0Sp2Y8s4ohgPLsZfHujakGqCVB+PyH2udG+x63eXbOFSVsW3bIcaO/ZyhQ0/l9tv7AjBmTG8fR6VUxR03URhjhjvv+qDn49m/Bvb9DmEx9pnYqlrLzy/kX/9awmOPLeLw4TxWrtzL6NHxhIUF+zo0pU5KuVc9icgZIhLlDP9NRCaLiB89uNqD1rxm39uN1F5iq7mlS5OIj5/Nvfd+zeHDeVx5ZSeWLbtFk4QKCO5cHjsDOCwi3YD7gW3AGx6Nyh9k7oGVRXdij/ZtLMpnsrLyGDfuc/r1e5WVK/fSokUcn39+Ne+8c7le0aQChjuJIt/YytwI4F/GmH9hL5Gt3ta9YTsBbDFM+3WqxsLCglm6dCdBQcIDD5zB2rVj9IomFXDc6T02XUQeAq4FzhKRYKB6X7ZRkAfL/2mHux9zUZgKcFu3HiIsLJjGjWMIDg7iP/8ZQWGhoWvXBr4OTSmPcOeMYiSQA9xkjNkDNAFe8GhUVd2WzyBzN9RqA63O93U0ykvy8gp44YVf6NTpFcaN+7z4+86d62uSUAHNnW7G94jIW0BvERkOLDPG/NfzoVVhiS/b966jQfQ5AdXB0qVJjBq1gFWr9gK2ySknJ5/wcHdOypXyb+5c9XQlsAy4Avvc7KUicrmnA6uy9q2E7d9BSCR0vsnX0SgPS03NZuzYz+jX71VWrTpSrJ4373JNEqracOcv/WGgtzFmH4CI1AO+Ad73ZGBV1u9ObaLzTRBRy7exKI/KzMylS5cZ7NiRRkhIEPfc04/HHuuvd1arasedRBFUlCQcKbhX2wg8uRmw4V07rP06BbyoqDCuuKIjixcnMWvWcLp00TqEqp7cSRRfishC7HOzwRa3Py9j+sC1cibkZ0Hj06F2W19HoypZXl4BU6YsoWPHelxwgf33feaZcwgNDSYoSLsCV9WXO8Xs+0TkUuBMbH9Ps40xH3k8sqomPxt+e84O953g21hUpVuyJInRo22xulmzWDZubEVERIjWIZSi7OdRtAFeBE4FVgP3GmN2eiuwKmf9/yBrP9TrDi31kthAkZqazYQJ3zJjRgLGQMuWcbzyygVERGiCUKpIWf8bXgP+C/wIXAi8DFzqjaCqnMICWPq0HY6/G/SJZH7PGMP7769j/Pgv2bMng5CQIO69tx+PPqrFaqVKKitRxBhj/u0MbxCR370RUJW0dSGkboHYFtD+al9HoypBdnY+99zzFXv2ZNCvX1MtVitVhrISRYSI9ODIcygiXT8bY6pH4jAGfnnUDne5GYK0N1B/lZdXQH5+IZGRoURGhjJr1nC2b0/l73/vpcVqpcpQVqLYDUx2+bzH5bMBBnkqqCplz2/2mRPhcdDrbl9HoyqoqFg9eHBLXnppKIB23qeUm8p6cNFAbwZSZf3hXBXc6XoIreHbWNQJS03N5qGHvmXmTFuszsrK4+mnz9FitVInoHreOOeujN2wdq4dbjfSp6GoE2OM4b331tK+/XRmzEggODiIhx46k8TEWzVJKHWCPJooRGSYiGwQkc0i8mAZ0/UWkYIq14fUD/dCziFofg40Os3X0Sg3ZWXlMXz421x55fvs2ZPB6ac3Y8WK0TzzzDl6RZNSFeCxQyvnuRXTgSFAEvCbiMw3xqwrZbrngIWeiqVC9i6HP/4HweEwZJZeEutHIiNDiYgIoWbNcJ5/fgi33NJTi9VKnYRyE4WICHAN0MoY86TzvOyGxphl5czaB9hsjNniLGce9il560pMdzvwAdD7RIP3qGXOXdjdx0Hcqb6NRZVryZIkatQILX4uxPTp9qbIhg2jfRmWUgHBnaanV4B+wFXO53TsmUJ5mgA7XD4nOd8VE5EmwCXAzLIWJCKjRCRBRBKSk5PdWPVJSl4NG9+DoBDoqZ3/VWWHDmUzZsxnnH76q9x883wKCgoBmyA0SShVOdxpeuprjOkpIisAjDEHRSTMjflKO9c3JT5PAR4wxhRIGU07xpjZwGyA+Pj4ksuofEuesu9dboHY5h5fnTpxtli9jjvuOHJn9ZAhrcjPLyQ4WK/RUKoyuZMo8pw6goHi51EUujFfEtDM5XNTYFeJaeKBeU6SqAucLyL5xpiP3Vi+ZxzYCBvfh+Aw6Puwz8JQx/fXXwcZM+ZzvvxyMwCnn96MWbOG07lzfR9HplRgcidRTAU+AuqLyNPA5cAjbsz3G9BGRFoCO4H/A47q/8IY07JoWETmAgt8miQAfn0cMPZy2JimPg1FHSs7O59+/V5l795M4uIieO65wVqsVsrD3Olm/C0RWQ6cg21OutgYs96N+fJFZBz2aqZg4DVjzFoRudUZX2ZdwidSt8LGd21t4oxJvo5GlSIiIoSHHz6LxYuTmDx5qNYhlPICMabsJn/nKqdjGGO2eySicsTHx5uEhATPLPznR2wvsR2ugfPf9Mw61Ak5dCibhx76hk6d6jNuXB/A1ifKqmkppY4lIsuNMfEVmdedpqfPsPUJASKAlsAGoFNFVlhl5R2GVbPtcJdbfBuLwhjDu++u5Y47vmTv3kxq147kxhu7ExUVpklCKS9zp+mpi+tnEekJjPZYRL6y9nXISob6PaBpf19HU60dr1gdFeXOxXZKqcp2wndmG2N+F5GqdXPcySosOPKY0/j79C5sH8nPL+Sll37liSd+ICsrn7i4CJ5/fjA336zFaqV8yZ07s1371g4CegJeuOvNi/78BNK2Qewp0O5KX0dTbYnABx+sJysrn6uv7sLkyefSoIEWq5XyNXfOKGJchvOxNYsPPBOODxgDy561w73u0gcTedmhQ9nk5OTToEE0wcFBzJlzEXv2ZHDuudptilJVRZmJwrnRLtoYc5+X4vG+vcvtw4nCa0KXv/s6mmrDtVh9+unN+PBD2417164NivtrUkpVDcdNFCIS4twL0dObAXndauex4B3+pg8m8pItWw4yZsxnLFz4JwDJyYfJyMglOlqL1UpVRWWdUSzD1iMSRWQ+8B6QWTTSGPOhh2PzvLzD8Mc8O9w18C7kqmry8gp46aXFPPHED2Rn22L1Cy8M4aabemixWqkqzJ0aRW0gBfuM7KL7KQzg/4li7euQmwYNe0O9LuVPryosN7eAvn3nkJi4B4BrrunCSy9psVopf1BWoqjvXPG0hiMJoojne3D1hqIb7HrdXfZ06qSFhQUzaFAL0tNzmDHjAoYM0WK1Uv6irEQRDETjXnfh/mdPAiQnQkQtaH2Jr6MJOMYY3nlnLXFxEQwb1hqAp54axKRJg4iM1MeRKuVPykoUu40xT3otEm9b94Z9b381hIT7NpYA41qsbtYslnXrxhIdHabPq1bKT5WVKAK3uph9ENa8aoc73+TbWAJIacXqxx7rrwlCKT9XVqI4x2tReNvyyZCXCc0HQ4PAvvrXW379dQejRy9gzZp9gBarlQokx00UxpgD3gzEa/IOQ+Irdvg0d56/pMqTl1fA1Vd/wLZtqZx6ai0tVisVYE64U0C/t+lDyD4A9bpD07N9HY3fMsaQn19IaGgwoaHBTJt2PkuWJPHww2dpsVqpAFP9nkL/x//se7fR2ktsBf355wGGDXuLBx/8pvi74cPb6hVNSgWo6pUoDmyEv76EoFBofbGvo/E7ubkF/OMfP9G58wy++upP3nhjFWlpOb4OSynlYdWr6WnlK4CxjzqNaujraPzKL79sZ/ToBaxda3uY/9vfuvLSS+cSG6uXFisV6KpPosjPtl12APQY59tY/Eh+fiFjx37G7Nm/A9C6dW1mzLiAwYNb+TgypZS3VJ9EselDyDkE9XtCg16+jsZvhIQEsX9/FqGhQTzwwBlMmKDFaqWqm+qTKFZMs++db/RtHH7gzz8PkJNTQMeO9QB4+eXzeOqpgcWflVLVS/UoZh/cDLsXQ0gN6HS9r6OpsnJzC3jmGVusvv76jykoKASgceMYTRJKVWPV44xig/PMiTaXQlhM2dNWUz//bIvV69bZYnX79nU5fDiPmBgtVitV3VWPRLHxPfvebqRv46iCDh7M4oEHvuHf/9ZitVKqdIGfKDL3QvIqCA6DU4b4OpoqJT+/kD595rB58wFCQ4N48MEzmTDhLCIiAv/PQinlvsDfI/w53743HaDdiZcQEhLE+PF9eO+9dcyaNZwOHbQOoZQ6VjVIFJ/a97aX+TaOKiA3t4AXX/yV2rUjufXWeADGju3D2LF99JnVSqnjCuxEkXcYtn4JEgQtL/B1ND7lWqyOiQlj5MhO1KoVqQlCKVWuwE4UWxdCYR40iIeYJr6OxidKFqvbtKnNzJnDqVUr0seRKaX8RWAniqJmp9YjfBuHDxhjePvtNdx110L27cskNDSIhx46k4ce0mK1UurEBO4ewxjY/KEdbnOpb2PxgcJCw5QpS9i3L5Ozzz6FmTMv0GK1UqpCPHpntogME5ENIrJZRB4sZfw1IrLKef0qIt0qbeX7foecVIhuCrU7VNpiq7Lc3AIOHMgCIDg4iNmzL+TVVy/i+++v1yShlKowjyUKEQkGpgPnAR2Bq0SkY4nJ/gL6G2O6Ak8BsystgD8X2PcWQ6vFA4p+/nk7PXrM4u9//7T4u+7dG3LTTT20YK2UOimebHrqA2w2xmwBEJF5wAhgXdEExphfXaZfAjSttLUXNztdUmmLrIoOHMjigQe+Zs6cFYB9fvWBA1nUrq3FaqVU5fBk01MTYIfL5yTnu+O5GfiitBEiMkpEEkQkITk5ufw1H/rT3o0dFgPNB59AyP7DGMNbb62ifftpzJmzgtDQIB577GxWrbpNk4RSqlJ58oyitPYOU+qEIgOxieLM0sYbY2bjNEvFx8eXuoyjbPncvrc4LyDvxi4oKGT48Lf58svNAFqsVkp5lCfPKJKAZi6fmwK7Sk4kIl2BOcAIY0xKpay5qNuOFudWyuKqmuDgIDp2rEvt2pG89tpFLFqkxWqllOeIMeUfoFdowSIhwEbgHGAn8BtwtTFmrcs0zYHvgOtK1CuOKz4+3iQkJBx/gtwMeKUOFOTCbfugRmDsQH/6aRt5eYUMGtQSgIyMXLKy8qhXL8rHkSml/IGILDfGxFdkXo81PRlj8kVkHLAQCAZeM8asFZFbnfEzgceAOsArYq9Myq/oDym282ebJBrEB0SScC1WN2sWy7p1Y4mODit+KaWUp3n0hjtjzOfA5yW+m+kyfAtwS6WudMf39r35oEpdrLfZYvVq7r57IcnJhwkNDeLGG7sTElI9HkqolKo6Au/O7D3L7Huj03wbx0nYtCmF2277jG+//QuwxepZs4bTvn1dH0emlKqOAitRFOTC7iV2uMlZvo2lggoLDRde+DYbNqRQu3YkL710Ltdf3w2pBjcNKqWqpsBKFHt/h/xsqNUGavjX0bcxBhEhKEh48cVzef/9dbzwwhAtViulfC6wEkXSj/a9aX/fxnECDhzI4v77v6ZmzXBeemkoAMOHt2X48LY+jkwppazAShR7ltr3hn18G4cbSharIyNDePDBM/UMQilV5QROoigsOHLFU9OzfRtLOUoWqwcMaMHMmRdoklBKVUmBkyj2r4HsgxB7CtSqms02hYWGp5/+kaef/omcnALq1LHF6uuu02K1UqrqCpxEsc/2nkrDvlW2W/GgICExcS85OQXccEN3XnhhCHXr1vB1WEopVaYAShT2mdDUr7xnH1WGlJTDHDyYTevWtQGYOnUY48b1ZuDAlj6OTCml3BM4t/nuS7Tv9Xv6NIwixhjeeGMl7dtP56qrPqCgoBCAJk1iNUkopfxKYCQKYyA50Q7X8/0ZxaZNKQwe/AbXXfcx+/cfJjo6jIMHs30dllJKVUhgND2lbYXcdKhRH6Ib+SyMnJx8nn/+Fy1WK6UCSmAkij2/2ff6PXwWgjGG/v3nsnTpTgAtViulAkaAJArn+RQ+7AhQRLjmmi4cPJjNrFnDGTCghc9iUVVDXl4eSUlJZGdrs6PynoiICJo2bUpoaGilLTMwEsW+5fbdi2cUxhjefHMVeXmF3HSTXe+YMb35+997ERERGJtVnZykpCRiYmJo0aKFNj0qrzDGkJKSQlJSEi1bVt5FM/6/RzMGklfb4bpdvLLKjRvtndXfffcX0dFhnH9+Gxo2jCY4OIjg4MC4PkCdvOzsbE0SyqtEhDp16pCcnFypy/X/RJG+HbKSIaIO1Gzh0VXl5OTz3HO2WJ2ba4vVkycPpUED7XpDlU6ThPI2T/zN+X+iKDqbqN8NxHNH8z/8sJXRoxewYUMKoMVqpVT14f/tJDt/tu91OntsFcYY7r//GzZsSKFduzp8//31/Oc/IzRJqCovODiY7t2707lzZy688EIOHTpUPG7t2rUMGjSItm3b0qZNG5566imMMcXjv/jiC+Lj4+nQoQPt27fn3nvv9cEvKNuKFSu45ZbKfZpyZcrJyWHkyJG0bt2avn37snXr1lKne/vtt+nSpQtdu3Zl2LBh7N+/v3jcu+++S8eOHenUqRNXX301AMnJyQwbNswbP8EyxvjVq1evXuYob59pzIsYs3KWqUyFhYUmPT2n+PPvv+8yjz/+vcnOzqvU9ajAtW7dOl+HYKKiooqHr7vuOjNp0iRjjDGHDx82rVq1MgsXLjTGGJOZmWmGDRtmpk2bZowxZvXq1aZVq1Zm/fr1xhhj8vLyzPTp0ys1try8k/+/dPnll5vExESvrvNETJ8+3YwePdoYY8zbb79trrzyylJjqlevnklOTjbGGHPfffeZxx9/3BhjzMaNG0337t3NgQMHjDHG7N27t3i+G264wfz888+lrre0vz0gwVRwv+v/TU95h+17TLNKW+TGjSnceusC4uIi+PDDkQD06NGIHj18dzOf8nMveahWcY8pfxpHv379WLVqFQD/+9//OOOMMzj33HMBqFGjBtOmTWPAgAGMHTuW559/nocffpj27dsDEBISwpgxY45ZZkZGBrfffjsJCQmICI8//jiXXXYZ0dHRZGRkAPD++++zYMEC5s6dyw033EDt2rVZsWIF3bt356OPPiIxMZG4uDgAWrduzS+//EJQUBC33nor27dvB2DKlCmcccYZR607PT2dVatW0a2b7Y1h2bJl3HnnnWRlZREZGcl//vMf2rVrx9y5c/nss8/Izs4mMzOTTz/9lNtvv53Vq1eTn5/PxIkTGTFiBFu3buXaa68lMzMTgGnTpnH66ae7vX1L88knnzBx4kQALr/8csaNG1f8NMsiRTvjzMxM6tSpQ1paGq1btwbg3//+N2PHjqVWrVoA1K9fv3i+iy++mLfeeuuY7eIJ/p0oCnJh/2pAoPHJb6zSitW7dqXTuHHMyceqlA8VFBTw7bffcvPNNwO22alXr15HTXPqqaeSkZFBWloaa9as4Z577il3uU899RQ1a9Zk9WpbKzx48GC582zcuJFvvvmG4OBgCgsL+eijj7jxxhtZunQpLVq0oEGDBlx99dXcddddnHnmmWzfvp2hQ4eyfv36o5aTkJBA585Hmpzbt2/Pjz/+SEhICN988w0TJkzggw8+AGDx4sWsWrWK2rVrM2HCBAYNGsRrr73GoUOH6NOnD4MHD6Z+/fp8/fXXREREsGnTJq666ioSEhKOif+ss84iPT39mO9ffPFFBg8efNR3O3fupFkzexAbEhJCzZo1SUlJoW7dI49qDg0NZcaMGXTp0oWoqCjatGnD9OnTi7cVwBlnnEFBQQETJ04sbnKKj4/nkUceKXd7Vwb/ThQHNkBhHsSdCuGxJ7WoksXqG2/szvPPa7FaVZITOPKvTFlZWXTv3p2tW7fSq1cvhgwZAnDMUa2rE7lq5ptvvmHevHnFn4uOfMtyxRVXEBwcDMDIkSN58sknufHGG5k3bx4jR44sXu66deuK50lLSyM9PZ2YmCMHbbt376ZevXrFn1NTU7n++uvZtGkTIkJeXl7xuCFDhlC7tu3B+auvvmL+/Pm8+OKLgL2Mefv27TRu3Jhx48aRmJhIcHBw8U66pJ9++qnc31jEmGP/3Utu37y8PGbMmMGKFSto1aoVt99+O//4xz945JFHyM/PZ9OmTSxatIikpCTOOuss1qxZQ1xcHPXr12fXrl1ux3Iy/DtRHNpk32t3qPAijDGMGvUpc+bY51m0a1eHmTP1zmoVGCIjI0lMTCQ1NZXhw4czffp0xo8fT6dOnfjxxx+PmnbLli1ER0cTExNDp06dWL58eXGzzvEcL+G4flfyzvSoqCOXk/fr14/NmzeTnJzMxx9/XHyEXFhYyOLFi4mMjCzzt7ku+9FHH2XgwIF89NFHbN26lQEDBpS6TmMMH3zwAe3atTtqeRMnTqRBgwasXLmSwsJCIiIiSl3viZxRNG3alB07dtC0aVPy8/NJTU0tTlhFEhMTAXtGB3DllVfy7LPPFs9/2mmnERoaSsuWLWnXrh2bNm2id+/eZGdnl7l9KpN/X/V04A/7Hte6wosQEWJjwwkPD+bJJwewcuWtmiRUwKlZsyZTp07lxRdfJC8vj2uuuYaff/6Zb775BrBnHuPHj+f+++8H4L777uOZZ54pPqouLCxk8uTJxyz33HPPZdq0acWfi5qeGjRowPr164ublo5HRLjkkku4++676dChA3Xq1Cl1uUU7U1cdOnRg8+bNxZ9TU1Np0qQJAHPnzj3uOocOHcrLL79cfLS/YsWK4vkbNWpEUFAQb7zxBgUFBaXO/9NPP5GYmHjMq2SSALjooot4/fXXAVurGTRo0DGJtUmTJqxbt674Jrmvv/6aDh3swe/FF1/M99/bRzzv37+fjRs30qpVK8A2S7k2vXmSfyeKFOfUtHb7E5pt48YUfvppW/HnJ54YyKpVt/Hoo/0JD/fvkyyljqdHjx5069aNefPmERkZySeffMKkSZNo164dXbp0oXfv3owbNw6Arl27MmXKFK666io6dOhA586d2b179zHLfOSRRzh48CCdO3emW7duxTu1Z599luHDhzNo0CAaNSr7IpCRI0fy5ptvFjc7AUydOpWEhAS6du1Kx44dmTlz5jHztW/fntTU1OKj+/vvv5+HHnqouD3/eB599FHy8vLo2rUrnTt35tFHHwVgzJgxvP7665x22mls3LjxqLOQirr55ptJSUmhdevWTJ48ufhMAaB79+4ANG7cmMcff5yzzz6brl27kpiYyIQJEwCb1OrUqUPHjh0ZOHAgL7zwQnEy/f7777ngggtOOkZ3SGltaFVZfHy8KS4wTY2GvEy4chE061/uvDk5+Tz77M8888zP1K8fxbp1Y4iJCfdswKraWr9+ffGRofKMf/7zn8TExFTpeyk85eyzz+aTTz4ptS5U2t+eiCw3xsRXZF3+e0ZhDAQ5vSPWalvu5IsWbaVbt5lMnPgDubkFnHtuKwoK/CtJKqWOdttttxEeXv0O9pKTk7n77rvdunigMvhvO0vOIfsKjYKohsedbP/+w9x339fMnZsIQPv2dZk58wL692/hjSiVUh4UERHBtdde6+swvK5evXpcfPHFXluf/yaK1L/se82WcJzL+YwxDBv2JsuX7yY8PJiHHz6L++8/Q+sQymvKugxVKU/wRDnBf5ue0uwdm8Q0P+4kIsLEiQMYNKilFquV10VERJCSkuKR/7hKlcY4z6M43qW9FeW/e81se2McNY7c0l5UrM7Ozucf/7CXqg0f3pYLLmijR3XK65o2bUpSUlKlPxtAqbIUPeGuMvlvoijIte8hNnMuWrSVW2+1d1YHBwtjxvSmWbOagD4TQPlG0U1SSvk7jzY9icgwEdkgIptF5MFSxouITHXGrxKRnm4vvNAmiv3p4dx44ycMHPg6Gzak0L59Xb777vriJKGUUurkeOyMQkSCgenAECAJ+E1E5htj1rlMdh7Qxnn1BWY47+Uy+Tn897du3PNkHClpiYSHB/PII2dz332nax1CKaUqkSf3qH2AzcaYLQAiMg8YAbgmihHAf52+0peISJyINDLGHHsLaAlSmMf8de1ISRMGDWrJzJkX0KZNHU/8DqWUqtY8mSiaADtcPidx7NlCadM0AY5KFCIyChjlfMwQkQ0uo+t+9x3725Z/z12gqwvsL3eqwKfbwdLtcIRuC6td+ZOUzpOJorQKcsnrBN2ZBmPMbGB2qSsRSajobemBRLeDpdvB0u1whG4LS0SOfbiGmzxZzE4CXB871xQo2Xm6O9MopZTyIU8mit+ANiLSUkTCgP8D5peYZj5wnXP102lAqjv1CaWUUt7jsaYnY0y+iIwDFgLBwGvGmLUicqszfibwOXA+sBk4DNxYgVWV2iRVDel2sHQ7WLodjtBtYVV4O/hdN+NKKaW8y3/7elJKKeUVmiiUUkqVyS8ShUe7AvEjbmyHa5zfv0pEfhWRbr6I0xvK2xYu0/UWkQIRudyb8XmLO9tBRAaISKKIrBWRH7wdoze48X+jpoh8KiIrne1QkXpolScir4nIPhFZc5zxFdtXGmOq9AtbCP8TaAWEASuBjiWmOR/4AntfxmnAUl/H7aPtcDpQyxk+LxC3g7vbwmW677AXTVzu67h99DcRh+0Nobnzub6v4/bRdpgAPOcM1wMOAGG+jt0D2+JsoCew5jjjK7Sv9IcziuKuQIwxuUBRVyCuirsCMcYsAeJEpOwnuvufcreDMeZXY8xB5+MS7H0pgcidvwmA24EPgH3eDM6L3NkOVwMfGmO2AxhjAnFbuLMdDBAjtivpaGyiyPdumJ5njPkR+9uOp0L7Sn9IFMfr5uNEp/F3J/obb8YeOQSicreFiDQBLgFmejEub3Pnb6ItUEtEFonIchG5zmvReY8722Ea0AF7Q+9q4A5jTKF3wqtSKrSv9IduViutKxA/5/ZvFJGB2ERxpkcj8h13tsUU4AFjTEEAP4/Ene0QAvQCzgEigcUissQYs9HTwXmRO9thKJAIDAJOBb4WkZ+MMWkejq2qqdC+0h8ShXYFYrn1G0WkKzAHOM8Yk+Kl2LzNnW0RD8xzkkRd4HwRyTfGfOyVCL3D3f8b+40xmUCmiPwIdAMCKVG4sx1uBJ41tqF+s4j8BbQHlnknxCqjQvtKf2h60q5ArHK3g4g0Bz4Erg2wI8aSyt0WxpiWxpgWxpgWwPvAmABLEuDe/41PgLNEJEREamB7cF7v5Tg9zZ3tsB17VoWINMD2pLrFq1FWDRXaV1b5Mwrjva5AqjQ3t8NjQB3gFedIOt8EYK+Zbm6LgOfOdjDGrBeRL4FVQCEwxxhT6qWT/srNv4engLkishrb/PKAMSbguh4XkbeBAUBdEUkCHgdC4eT2ldqFh1JKqTL5Q9OTUkopH9JEoZRSqkyaKJRSSpVJE4VSSqkyaaJQSilVJk0UqkpyenxNdHm1KGPajEpY31wR+ctZ1+8i0q8Cy5gjIh2d4Qklxv16sjE6yynaLmuc3lDjypm+u4icXxnrVtWXXh6rqiQRyTDGRFf2tGUsYy6wwBjzvoicC7xojOl6Ess76ZjKW66IvA5sNMY8Xcb0NwDxxphxlR2Lqj70jEL5BRGJFpFvnaP91SJyTG+xItJIRH50OeI+y/n+XBFZ7Mz7noiUtwP/EWjtzHu3s6w1InKn812UiHzmPNtgjYiMdL5fJCLxIvIsEOnE8ZYzLsN5f8f1CN85k7lMRIJF5AUR+U3scwJGu7FZFuN06CYifcQ+g2SF897OuUv5SWCkE8tIJ/bXnPWsKG07KnUMX/efri99lfYCCrCduCUCH2F7EYh1xtXF3lladEac4bzfAzzsDAcDMc60PwJRzvcPAI+Vsr65OM+sAK4AlmI701sNRGG7pl4L9AAuA/7tMm9N530R9ui9OCaXaYpivAR43RkOw/bkGQmMAh5xvg8HEoCWpcSZ4fL73gOGOZ9jgRBneDDwgTN8AzDNZf5ngL85w3HYPp+ifP3vra+q/aryXXioaivLGNO96IOIhALPiMjZ2K4omgANgD0u8/wGvOZM+7ExJlFE+gMdgV+cbk3CsEfipXlBRB4BkrG9754DfGRsh3qIyIfAWcCXwIsi8hy2ueqnE/hdXwBTRSQcGAb8aIzJcpq7usqRJ/HVBNoAf5WYP1JEEoEWwHLga5fpXxeRNtjeQEOPs/5zgYtE5F7ncwTQnMDr/0lVIk0Uyl9cg30yWS9jTJ6IbMXu5IoZY350EskFwBsi8gJwEPjaGHOVG+u4zxjzftEHERlc2kTGmI0i0gvbZ84/ROQrY8yT7vwIY0y2iCzCdns9Eni7aHXA7caYheUsIssY011EagILgLHAVGxfRt8bYy5xCv+LjjO/AJcZYza4E69SoDUK5T9qAvucJDEQOKXkBCJyijPNv4FXsY+EXAKcISJFNYcaItLWzXX+CFzszBOFbTb6SUQaA4eNMW8CLzrrKSnPObMpzTxsZ2xnYTuyw3m/rWgeEWnrrLNUxphUYDxwrzNPTWCnM/oGl0nTsU1wRRYCt4tzeiUiPY63DqWKaKJQ/uItIF5EErBnF3+UMs0AIFFEVmDrCP8yxiRjd5xvi8gqbOJo784KjTG/Y2sXy7A1iznGmBVAF2CZ0wT0MDCplNlnA6uKitklfIV9tvE3xj66E+wzRNYBv4vIGmAW5ZzxO7GsxHar/Tz27OYXbP2iyPdAx6JiNvbMI9SJbY3zWaky6eWxSimlyqRnFEoppcqkiUIppVSZNFEopZQqkyYKpZRSZdJEoZRSqkyaKJRSSpVJE4VSSqky/T97o9KxESyGwAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "lw = 2\n",
    "plt.plot(fpr, tpr, color='darkorange',\n",
    "         lw=lw, label='ROC curve (area = %0.2f)' % aucroc)\n",
    "plt.plot([0, 1], [0, 1], color='navy', lw=lw, linestyle='--')\n",
    "plt.xlim([-0.01, 1.0])\n",
    "plt.ylim([0.0, 1.05])\n",
    "plt.xlabel('False Positive Rate')\n",
    "plt.ylabel('True Positive Rate')\n",
    "plt.title('Receiver operating characteristic')\n",
    "plt.legend(loc=\"lower right\")\n",
    "plt.savefig(\"ROC-MNIST-C\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## FashionMNIST"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"model_1\"\n",
      "__________________________________________________________________________________________________\n",
      "Layer (type)                    Output Shape         Param #     Connected to                     \n",
      "==================================================================================================\n",
      "input_1 (InputLayer)            [(None, 28, 28, 1)]  0                                            \n",
      "__________________________________________________________________________________________________\n",
      "conv2d (Conv2D)                 (None, 28, 28, 16)   144         input_1[0][0]                    \n",
      "__________________________________________________________________________________________________\n",
      "activation (Activation)         (None, 28, 28, 16)   0           conv2d[0][0]                     \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_1 (Conv2D)               (None, 28, 28, 80)   11520       activation[0][0]                 \n",
      "__________________________________________________________________________________________________\n",
      "activation_1 (Activation)       (None, 28, 28, 80)   0           conv2d_1[0][0]                   \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_2 (Conv2D)               (None, 28, 28, 80)   57600       activation_1[0][0]               \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_3 (Conv2D)               (None, 28, 28, 80)   1280        activation[0][0]                 \n",
      "__________________________________________________________________________________________________\n",
      "add (Add)                       (None, 28, 28, 80)   0           conv2d_2[0][0]                   \n",
      "                                                                 conv2d_3[0][0]                   \n",
      "__________________________________________________________________________________________________\n",
      "activation_2 (Activation)       (None, 28, 28, 80)   0           add[0][0]                        \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_4 (Conv2D)               (None, 28, 28, 80)   57600       activation_2[0][0]               \n",
      "__________________________________________________________________________________________________\n",
      "activation_3 (Activation)       (None, 28, 28, 80)   0           conv2d_4[0][0]                   \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_5 (Conv2D)               (None, 28, 28, 80)   57600       activation_3[0][0]               \n",
      "__________________________________________________________________________________________________\n",
      "add_1 (Add)                     (None, 28, 28, 80)   0           add[0][0]                        \n",
      "                                                                 conv2d_5[0][0]                   \n",
      "__________________________________________________________________________________________________\n",
      "activation_4 (Activation)       (None, 28, 28, 80)   0           add_1[0][0]                      \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_6 (Conv2D)               (None, 14, 14, 160)  115200      activation_4[0][0]               \n",
      "__________________________________________________________________________________________________\n",
      "activation_5 (Activation)       (None, 14, 14, 160)  0           conv2d_6[0][0]                   \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_7 (Conv2D)               (None, 14, 14, 160)  230400      activation_5[0][0]               \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_8 (Conv2D)               (None, 14, 14, 160)  12800       activation_4[0][0]               \n",
      "__________________________________________________________________________________________________\n",
      "add_2 (Add)                     (None, 14, 14, 160)  0           conv2d_7[0][0]                   \n",
      "                                                                 conv2d_8[0][0]                   \n",
      "__________________________________________________________________________________________________\n",
      "activation_6 (Activation)       (None, 14, 14, 160)  0           add_2[0][0]                      \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_9 (Conv2D)               (None, 14, 14, 160)  230400      activation_6[0][0]               \n",
      "__________________________________________________________________________________________________\n",
      "activation_7 (Activation)       (None, 14, 14, 160)  0           conv2d_9[0][0]                   \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_10 (Conv2D)              (None, 14, 14, 160)  230400      activation_7[0][0]               \n",
      "__________________________________________________________________________________________________\n",
      "add_3 (Add)                     (None, 14, 14, 160)  0           add_2[0][0]                      \n",
      "                                                                 conv2d_10[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "activation_8 (Activation)       (None, 14, 14, 160)  0           add_3[0][0]                      \n",
      "__________________________________________________________________________________________________\n",
      "average_pooling2d (AveragePooli (None, 1, 1, 160)    0           activation_8[0][0]               \n",
      "__________________________________________________________________________________________________\n",
      "flatten (Flatten)               (None, 160)          0           average_pooling2d[0][0]          \n",
      "__________________________________________________________________________________________________\n",
      "dense (Dense)                   (None, 10)           1610        flatten[0][0]                    \n",
      "==================================================================================================\n",
      "Total params: 1,006,554\n",
      "Trainable params: 1,006,554\n",
      "Non-trainable params: 0\n",
      "__________________________________________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "ebm_model_fm = create_wide_residual_network((28, 28, 1), nb_classes=10, N=2, k=5)\n",
    "ebm_model_fm.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## FashionMNIST Classifier for IS/FID"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def vgg_block(layer_in, n_filters, n_conv):\n",
    "    # Add convolutional layers\n",
    "    for _ in range(n_conv):\n",
    "        layer_in = keras.layers.Conv2D(n_filters, (3,3), padding='same', activation='relu')(layer_in)\n",
    "    # Add max pooling layer\n",
    "    layer_in = keras.layers.MaxPooling2D((2,2), strides=(2,2))(layer_in)\n",
    "    return layer_in"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"model_2\"\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "input_2 (InputLayer)         [(None, 28, 28, 1)]       0         \n",
      "_________________________________________________________________\n",
      "conv2d_11 (Conv2D)           (None, 28, 28, 128)       1280      \n",
      "_________________________________________________________________\n",
      "conv2d_12 (Conv2D)           (None, 28, 28, 128)       147584    \n",
      "_________________________________________________________________\n",
      "conv2d_13 (Conv2D)           (None, 28, 28, 128)       147584    \n",
      "_________________________________________________________________\n",
      "max_pooling2d (MaxPooling2D) (None, 14, 14, 128)       0         \n",
      "_________________________________________________________________\n",
      "conv2d_14 (Conv2D)           (None, 14, 14, 256)       295168    \n",
      "_________________________________________________________________\n",
      "conv2d_15 (Conv2D)           (None, 14, 14, 256)       590080    \n",
      "_________________________________________________________________\n",
      "conv2d_16 (Conv2D)           (None, 14, 14, 256)       590080    \n",
      "_________________________________________________________________\n",
      "max_pooling2d_1 (MaxPooling2 (None, 7, 7, 256)         0         \n",
      "_________________________________________________________________\n",
      "flatten (Flatten)            (None, 12544)             0         \n",
      "_________________________________________________________________\n",
      "dense_1 (Dense)              (None, 10)                125450    \n",
      "=================================================================\n",
      "Total params: 1,897,226\n",
      "Trainable params: 1,897,226\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "input_ = keras.layers.Input(shape=(28, 28, 1))\n",
    "vgg_1 = vgg_block(input_, 128, 3) # 14, 14, 128\n",
    "vgg_2 = vgg_block(vgg_1, 256, 3) # 7, 7, 256\n",
    "flatten = keras.layers.Flatten(name='flatten')(vgg_2)\n",
    "output = keras.layers.Dense(10, activation='softmax')(flatten)\n",
    "model = keras.Model(inputs=input_, outputs=output)\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_valid, X_train = X_train_full_fm[:5000], X_train_full_fm[5000:]\n",
    "y_valid, y_train = y_train_full_fm[:5000], y_train_full_fm[5000:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/10\n",
      "1719/1719 [==============================] - 31s 9ms/step - loss: 0.5582 - accuracy: 0.7955 - val_loss: 0.2825 - val_accuracy: 0.8968\n",
      "Epoch 2/10\n",
      "1719/1719 [==============================] - 16s 9ms/step - loss: 0.2651 - accuracy: 0.9024 - val_loss: 0.2474 - val_accuracy: 0.9138\n",
      "Epoch 3/10\n",
      "1719/1719 [==============================] - 15s 9ms/step - loss: 0.2079 - accuracy: 0.9247 - val_loss: 0.2167 - val_accuracy: 0.9186\n",
      "Epoch 4/10\n",
      "1719/1719 [==============================] - 16s 9ms/step - loss: 0.1736 - accuracy: 0.9372 - val_loss: 0.2083 - val_accuracy: 0.9220\n",
      "Epoch 5/10\n",
      "1719/1719 [==============================] - 16s 9ms/step - loss: 0.1470 - accuracy: 0.9475 - val_loss: 0.2390 - val_accuracy: 0.9212\n",
      "Epoch 6/10\n",
      "1719/1719 [==============================] - 16s 9ms/step - loss: 0.1171 - accuracy: 0.9581 - val_loss: 0.2145 - val_accuracy: 0.9278\n",
      "Epoch 7/10\n",
      "1719/1719 [==============================] - 16s 9ms/step - loss: 0.0913 - accuracy: 0.9669 - val_loss: 0.2605 - val_accuracy: 0.9188\n",
      "Epoch 8/10\n",
      "1719/1719 [==============================] - 16s 9ms/step - loss: 0.0727 - accuracy: 0.9738 - val_loss: 0.2931 - val_accuracy: 0.9176\n",
      "Epoch 9/10\n",
      "1719/1719 [==============================] - 16s 9ms/step - loss: 0.0604 - accuracy: 0.9772 - val_loss: 0.2939 - val_accuracy: 0.9212\n",
      "Epoch 10/10\n",
      "1719/1719 [==============================] - 16s 9ms/step - loss: 0.0494 - accuracy: 0.9826 - val_loss: 0.3273 - val_accuracy: 0.9236\n"
     ]
    }
   ],
   "source": [
    "model.compile(loss=\"sparse_categorical_crossentropy\",\n",
    "              optimizer=\"adam\", metrics=[\"accuracy\"])\n",
    "early_stopping = keras.callbacks.EarlyStopping(patience=10, \n",
    "                                               restore_best_weights=True)\n",
    "history = model.fit(X_train, y_train, epochs=10,\n",
    "                    validation_data=(X_valid, y_valid),\n",
    "                    callbacks=[early_stopping])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "optimizer = keras.optimizers.Adam(1e-4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "jem_fm = JEM(ebm_model_fm, optimizer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "history_fm = jem_fm.fit(X_train_full_fm, y_train_full_fm, 32, 25, optimizer, 0.0, 1.0, num_steps_markov=tf.constant(120),\n",
    "        var=tf.constant(1e-2 ** 2), step_size=tf.constant(2.0), callbacks_energy=[],\n",
    "        metrics_samples=[(\"IS\", is_metric_callback), (\"FID\", fid_metric_callback)],\n",
    "        alpha=tf.constant(0.0), clip_thresh=tf.constant(1e6),\n",
    "        weight_ce_loss=tf.constant(1.0), save_best_weights=True, use_replay_buffer=True)"
   ]
  }
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