From b3c95a095e89b5c370a4094a29b25c2b7edaaf60 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=D0=9C=D0=B8=D1=85=D0=B0=D0=B8=D0=BB=20=D0=A2=D0=B5=D1=80?=
 =?UTF-8?q?=D0=B5=D1=88=D0=BA=D0=B8=D0=BD?=
 <mihailtereskin@MacBook-Pro-Mihail.local>
Date: Fri, 21 Aug 2020 17:02:20 +0300
Subject: [PATCH 1/8] Example of applying different calibration methods

---
 examples/calibration_example.ipynb | 2361 ++++++++++++++++++++++++++++
 examples/calibrator.py             |  211 +++
 2 files changed, 2572 insertions(+)
 create mode 100644 examples/calibration_example.ipynb
 create mode 100644 examples/calibrator.py

diff --git a/examples/calibration_example.ipynb b/examples/calibration_example.ipynb
new file mode 100644
index 0000000..f9e6227
--- /dev/null
+++ b/examples/calibration_example.ipynb
@@ -0,0 +1,2361 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 50,
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/",
+     "height": 34
+    },
+    "colab_type": "code",
+    "id": "s0rU2DMvB2rL",
+    "outputId": "b11f83ea-ae50-4f8e-92a4-0d585da2f5be"
+   },
+   "outputs": [],
+   "source": [
+    "from sklearn.metrics import accuracy_score\n",
+    "from scipy.special import softmax\n",
+    "import calibrator\n",
+    "import numpy as np\n",
+    "import pandas as pd\n",
+    "from sklearn.neural_network import MLPClassifier\n",
+    "from sklearn.calibration import calibration_curve\n",
+    "import matplotlib.pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/",
+     "height": 1000,
+     "referenced_widgets": [
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+    "colab_type": "code",
+    "id": "ygJyUrpkB2rR",
+    "outputId": "2eb7ae89-c6a2-454f-8f91-ca05c6a6cf3c"
+   },
+   "outputs": [],
+   "source": [
+    "test_data = pd.read_csv('mnist_test.csv')\n",
+    "train_data = pd.read_csv('mnist_train.csv')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "colab": {},
+    "colab_type": "code",
+    "id": "I5XO9RDjB2rU"
+   },
+   "outputs": [],
+   "source": [
+    "y_test = test_data['label']\n",
+    "y_train = train_data['label'][0:48000]\n",
+    "X_test = test_data.drop(columns=['label'])\n",
+    "X_train = train_data.drop(columns=['label'])\n",
+    "X_train = X_train[0:48000][:]\n",
+    "cal = train_data[48000:][:]\n",
+    "y_cal = cal['label']\n",
+    "X_cal = cal.drop(columns=['label'])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/",
+     "height": 153
+    },
+    "colab_type": "code",
+    "id": "8qM2NebHB2ra",
+    "outputId": "eaea1671-b680-489a-8cb6-68a734ab759e"
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "MLPClassifier(activation='relu', alpha=0.0001, batch_size='auto', beta_1=0.9,\n",
+       "              beta_2=0.999, early_stopping=False, epsilon=1e-08,\n",
+       "              hidden_layer_sizes=(100, 100), learning_rate='constant',\n",
+       "              learning_rate_init=0.001, max_fun=15000, max_iter=300,\n",
+       "              momentum=0.9, n_iter_no_change=10, nesterovs_momentum=True,\n",
+       "              power_t=0.5, random_state=1, shuffle=True, solver='adam',\n",
+       "              tol=0.0001, validation_fraction=0.1, verbose=False,\n",
+       "              warm_start=False)"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "clf = MLPClassifier((100, 100,), max_iter=300, random_state=1)\n",
+    "clf.fit(X_train, y_train)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "colab": {},
+    "colab_type": "code",
+    "id": "5hBUkdNCHyAs"
+   },
+   "outputs": [],
+   "source": [
+    "clf.out_activation_ = 'identity'\n",
+    "logits = clf.predict_proba(X_cal)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 51,
+   "metadata": {
+    "colab": {},
+    "colab_type": "code",
+    "id": "0Qp6L3N8IC-c"
+   },
+   "outputs": [],
+   "source": [
+    "calibr = calibrator.Calibrator(logits, y_cal)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 57,
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/",
+     "height": 34
+    },
+    "colab_type": "code",
+    "id": "nkE0lL29Jo6T",
+    "outputId": "9e845720-4268-4709-ef4e-e7b0998f61f2"
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "tensor([0.0244])"
+      ]
+     },
+     "execution_count": 57,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "test_logits = clf.predict_proba(X_test)\n",
+    "test_preds = softmax(test_logits, axis=1)\n",
+    "calibr.compute_ece(15, test_logits, y_test.to_numpy(), len(y_test))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/",
+     "height": 34
+    },
+    "colab_type": "code",
+    "id": "McvVpiIqR6Nj",
+    "outputId": "ed044e56-c766-457d-942a-7af91ac419f8"
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "tensor(0.0211, dtype=torch.float64)"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "calibr.ComputeTace(0.9, test_data, test_logits, 15, 'label')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "tensor([0.0025])"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "calibr.compute_sce(15, 'label', test_logits, test_data)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "tensor(0.0251, dtype=torch.float64)"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "calibr.ComputeAce(15, test_data, 'label', test_logits)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/",
+     "height": 34
+    },
+    "colab_type": "code",
+    "id": "rUPNsBe5WHet",
+    "outputId": "52673060-ebb3-4b6f-8dc9-f3d38ed980ef"
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "tensor([0.0148])"
+      ]
+     },
+     "execution_count": 40,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "calibr.TemperatureScaling()\n",
+    "new_logits = calibr.scale_logits_with_temperature(test_logits).detach().numpy()\n",
+    "calibr.compute_ece(15, new_logits, y_test.to_numpy(), len(y_test))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 58,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "tensor(0.0092, dtype=torch.float64)"
+      ]
+     },
+     "execution_count": 58,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "calibr.ComputeTace(0.9, test_data, new_logits, 15, 'label')\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 59,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "tensor(0.0231, dtype=torch.float64)"
+      ]
+     },
+     "execution_count": 59,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "calibr.ComputeAce(15, test_data, 'label', new_logits)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 60,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "tensor([0.0021])"
+      ]
+     },
+     "execution_count": 60,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "calibr.compute_sce(15, 'label', new_logits, test_data)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0.01349574089747102"
+      ]
+     },
+     "execution_count": 37,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "new_probs = calibrator.multiclass_histogram_binning(15, logits, y_cal.to_numpy(), test_logits)\n",
+    "\n",
+    "def SplitIntoBins(m, preds, labels):\n",
+    "    bins = []\n",
+    "    true_labels_for_bins = []\n",
+    "    for i in range(m):\n",
+    "            bins.append([])\n",
+    "            true_labels_for_bins.append([])\n",
+    "    for j in range(len(labels)):\n",
+    "            max_p = max(preds[j])\n",
+    "            for i in range(m):\n",
+    "                if i/m < max_p and max_p <= (i+1)/m:\n",
+    "                    bins[i].append((preds[j]))\n",
+    "                    true_labels_for_bins[i].append(labels[j])\n",
+    "    return bins, true_labels_for_bins\n",
+    "\n",
+    "def ComputeEce(m, preds, labels):\n",
+    "    bins, true_labels_for_bins = SplitIntoBins(m, preds, labels)\n",
+    "    accuracies = []\n",
+    "    confidences = []\n",
+    "    ece = 0\n",
+    "    bins = list(filter(None, bins))\n",
+    "    true_labels_for_bins = list(filter(None, true_labels_for_bins))\n",
+    "    for i in range(len(bins)):\n",
+    "        accuracy = accuracy_score(true_labels_for_bins[i], np.argmax(bins[i], axis=1))\n",
+    "        accuracies.append(accuracy)\n",
+    "        max_pi = sum(np.amax(bins[i], axis = 1))\n",
+    "        confidences.append(max_pi/len(bins[i]))\n",
+    "        ece += len(bins[i]) * abs(accuracies[i] - confidences[i])/2897\n",
+    "    return ece\n",
+    "ComputeEce(15, new_probs, y_test.to_numpy())"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/",
+     "height": 85
+    },
+    "colab_type": "code",
+    "id": "uUSoNf8XoWHp",
+    "outputId": "0a716825-bf17-4344-92c6-54dec28aba40"
+   },
+   "outputs": [],
+   "source": [
+    "y_true = []\n",
+    "for i in range(10):\n",
+    "    y_true.append([])\n",
+    "for i in range(10):\n",
+    "    for label in y_test:\n",
+    "        if label == i:\n",
+    "            y_true[i].append(1)\n",
+    "        else:\n",
+    "            y_true[i].append(0)                    "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 45,
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/",
+     "height": 34
+    },
+    "colab_type": "code",
+    "id": "gpigDxzW1NzT",
+    "outputId": "ee75b408-7706-4a8d-b897-9d2b5e951606"
+   },
+   "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"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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nCnSRALP3SDYjE9cyK2kHzWqF896tCWfWTKugHb84jbUOpUKPF+Gie9VYqxRToIsEkDyXZcBbP5B2MItHujfh7isaUj74LDp8WAs/T4A5j0JYJNw2B+I6eL5g8SgFukgA2JWeRVRlp5nWP65uSd3qlWhc8yz7jR/LhNl/h18+hgad4br3nFCXUk/NuUT8mMtlmbh0K11f+56Plm0FoHOz6LMP870b4L2u8Msn0OkJ5+KnwtxvaIQu4qc27TnC8Gmr+XHzfi5tFEmnptHn9oZrp8PMvzi37d88FRp19UyhUmIU6CJ+6LPl23hm5loqlAvi5QFtuP6Cumd+t+dxWxY70xFTf4S67Z3GWlXrerReKRkKdBE/VLd6KJ2aOs20oqu42Uwr5yikp8HhHc5/09Oc5eGSZwIWgso5jbUU5n5LgS7iB7Jz8/jvtxsAeKRHoWZa1jp3bqanOet2Hk77M7D/CPDtzkLNhQVXAOyf75OyFOIvKZmDEo9ToIuUZq48ktb/xtufLyLv4HZ61XNhvzaYgqPs9DTIPXrya8OioUptqBYHsR2cz6vEQHj+f6vUht2/wvi+kHcMgkMg/rKSP0bxGGOt9cmOExIS7IoVK3yyb5FSIScrfzSdH86FRtau9DQ4vIsg8k58XVB5J4zD6xQK6Tp/flSuBeVC3Ksj5UfYstAJ89j2nj9O8ShjzE/W2oSinnNrhG6M6Qn8GwgG3rPWvlTENgOBkTh/v/1irb3xrCsW8WfWQtahQiGdf9qj4Mj66P6TXxsSnh/SdThS5xI+/DWXuLiGdL2oLZUi6jrhHVoDgjw44zi2vYI8QBQb6MaYYOBN4EogFVhujEm01iYX2KYx8ARwibX2gDHmHOdPifjYqUatrjzI2OOEc1Ej6+OBnZN58nuGRTkj6aqxzntWqZM/ys7/CK/NIVclZq/ewY0d4qgCXJeeRU13L3pKmefOCL09sMFauwnAGPMp0A9ILrDNXcCb1toDANba3Z4uVKTEpPwI46921skMCoa4iyE3K/+C4w6whU+BlPvz9Eet1tC4xx+j7D8CO7wWlKtw2t1+uWYnT8/8kf0Zx+jQIIKGUZUV5nJG3An0GCClwONUoHBThyYAxpjFOKdlRlprvyz8RsaYYcAwgLi4uLOpV8T7Vk92AhzAletcOKzZEupf9sdI+o+LilViIDTynE6B7D6cxcjEtcxZvZMWtavw/m0X0jDqLJtpSZnmTqAXdbdC4Sup5YDGQCegLrDQGNPKWnvwhBdZOwYYA85F0TOuVsTbVn4IP33gfG6CnGl9gz/x2jnmPJdl4NtLSDuUxaM9mjLs8gZn10xLBPcCPRWILfC4LpBWxDZLrbU5wGZjzHqcgF/ukSpFvC0nC754DH4eD/Uvd1av37XGazM/dhw6Ss3wik4zrb4tia0eevYtbkXyuRPoy4HGxpj6wHZgEFB4BssMYDDwgTEmEucUzCZPFiriNQe3wWdDYMcquPQh6PwUBJeDJj08viuXyzJhyRZenrue4b2accvF8XQ+1x4sIvmKDXRrba4x5gFgLs758XHW2rXGmOeAFdbaxPznuhtjkoE84FFr7T5vFi7iERu+gal3OrNXBn0Mzfp4b1e7jzB8ahIrth7g8iZRdGmmIBfP0o1FUja5XLDwVZj3AkS3gBsmQo2GXtvdpz9u45nEtVQqH8wzV7Wgf7uYs2+mJWXaOd9YJBJQMvfD9Lvh96+gzQ1w1WgICfPqLuNqhNKteTTP9m1FVPjppy+KnC0FupQtO36Bz2525pT3fhUuvNMra2Rm5eTxn29/B+Cxns3o2DCSjg21UIR4lwJdyo6VH8Ksh50VeG7/AmIv9MpuVmzZz2NTk9i0J4NBF8ZirdXpFSkRCnQJfIWnJA543yvLqh3JzuWVL9cxYelWYqpVYsId7bm8SZTH9yNyKgp0CWynmpLoBTsPHeXT5SncenE8j/ZoSlgF/XpJydJPnASuEpiSeCDjGLNW72DIRfVoFB3Owsc6u7+CkIiHKdAl8LhcsOAVmP+i16YkWmv5Ys1Onpm5hoOZOXRsWIOGUZUV5uJTCnQJLCUwJXF3ehZPz1zD3LW7aB1TlQl3dFAzLSkVFOgSOEpgSmKey3L9O0vYeSiLJ3o1Y+il9SmnZlpSSijQJTB4eUpi2sGj1KriNNN6rl8rYqtXooFG5VLKaGgh/i0nCxIfhJn3Q1wHuHuBR8M8z2V5f/Fmur72PR8u2wrAFU2iFOZSKmmELv7rwFaYdEv+lMSHoctTzgpDHrJh92Eem5LEz9sO0qlpFF2b1/TYe4t4gwJd/NPv38A0701J/HjZNkYmriWsQjCjbziPa85XMy0p/RTo4l9KYEoiQHxkKN1b1mRk35ZEVlYzLfEPCnTxHydNSXwDQkI98tZZOXmM/uY3DIbhvdRMS/yTAl38Q9oqmDTEK1MSl23ax/Bpq9m8N4ObOsSpmZb4LQW6lH4/T4TZf/f4lMTDWTn868t1fLh0G3ERoXx8Zwc6NtKoXPyXAl1Kr5ws+OJR+HkC1L8CBozzaJfEXenZTPkplTsvrc/D3ZsQGqJfB/Fv+gmW0slLUxL3ZxxjdlIaQy6Op1F0ZRY+1kUrCEnAUKBL6eOFKYnWWmYl7WBk4lrSs3K4pFEkDaIqK8wloCjQpfTw0pTEXelZjJi+hm9+3UWbulX5aEAH3ekpAUmBLqVD5n6YNgw2fA1tBuV3STz3KYl5LsvA/GZaI3o35/ZL4tVMSwKWAl18r+CUxD6vQcLQc56SmHogk9pVKxEcZBjVrxVxEaHER3q2ja5IaaOhivjWzxNhbHfnfPkdX57z/PI8l+W9hZvo9vr3fLjUaaZ1eZMohbmUCRqhi294YUri+p2HeWxqEr+kHKRrs2i6t1QzLSlbFOhS8rwwJfHDpVt59vO1hFcsz78HnU/f8+robk8pcxToUrL+mJLo8siUxOO36TeKrkzv1rV55qoW1FAzLSmjFOhSMlwuWPAyzH8JaraEgRPOaUri0WN5vP71eoKCDE/0as5FDWpwUYMaHixYxP8o0MX7PDwlccnGfQyflsTWfZkMuaiemmmJ5FOgi3d5cEpielYOL85Zxyc/bqNejVA+vquDWtyKFKBAF+/5eQLMfsSZvXLHl1A34Zzebnd6NjNWbmfY5Q14qFsTKoV4brk5kUDg1jx0Y0xPY8x6Y8wGY8zw02w3wBhjjTHn9psr/i0nC2Y+AIl/gXoXOws3n2WY7zuSzQeLNwPQKLoyix7vzJO9myvMRYpQ7AjdGBMMvAlcCaQCy40xidba5ELbhQMPAsu8Uaj4iQNbnVMsO36By/4OnUec1ZREay2Jv6QxMnEtR7JzubxJFA2iKmsGi8hpuHPKpT2wwVq7CcAY8ynQD0gutN0o4GXgEY9WKP7jhCmJn0Cz3mf1NmkHj/LUjDV8t24358dW4+UBbdRMS8QN7gR6DJBS4HEq0KHgBsaYtkCstXaWMeaUgW6MGQYMA4iLizvzaqV08uCUxNw8F4PGLGXP4WyevqoFt3WMJzhIM1hE3OFOoBf122T/eNKYIGA0cFtxb2StHQOMAUhISLDFbC7+wENTElP2Z1KnWiXKBQfxwrWtiYsIJa6GZxaAFikr3LkomgrEFnhcF0gr8DgcaAXMN8ZsAS4CEnVhtAxIWwVjroBN86HP63Dt22cc5rl5LsYs2Ei3179n4pItAFzaOFJhLnIW3BmhLwcaG2PqA9uBQcCNx5+01h4C/pgMbIyZDzxirV3h2VKlVPHAlMRfd6Tz+NQkklIPcWWLmvRqXdsLhYqUHcUGurU21xjzADAXCAbGWWvXGmOeA1ZYaxO9XaSUIjlZMOcRWDkRGnSC68aeVZfEiUu28OznyVStVJ7/3diWPq1r625PkXPk1o1F1to5wJxCX3vmFNt2OveypFTywJTE47fpN6kZztXn1eHpq1oQERbipYJFyhbdKSru+f1rmHonWHtWUxIzj+Xy6tzfKBdseLJ3czo0qEEHNdMS8SitWCSn53LBvBfho+uhal0YNu+Mw3zxhr30eGMB4xZv5liuC2s1wUnEGzRCl6Kl/Ai/fwUb58H2FXDeYGcmyxnMYjl0NIcXZv/KZytSqB8ZxqS7L6Z9/QgvFi1StinQ5WQpP8IHV0FetvO444Nw5XNn3CVx75FsPk9K454rGvK3bo2pWF79V0S8SYEuJ7IWFo3+M8xNEFSq5naY7zmczee/pHHHpfVpGFWZRY930UVPkRKiQJc/ZR+BWQ/B+jlOkGMgOATiLyv2pdZaZqzazrOfJ5OZnUfnZtHUjwxTmIuUIAW6OPash8+GwN7foPNTTohvW+z8N7b9aV+6/eBRRkxfzfz1e2gX5zTTqh8ZVkKFi8hxCnSB1VMg8UEoXwmGTIeGnZ2v17uo2Jc6zbSWsO/IMUZe3YIhF6uZloivKNDLstxsmPskLH8P4i6GAeOgSh23XrptXyYx1Z1mWi/1b0NcRCixEeq/IuJLmodeVh3YCuN6OGHe8S9w6+duhXlunou35m+k2+jvmbBkCwCXNIpUmIuUAhqhl0Xrv4TpdzszWm74CJpf5dbL1qYd4vGpSazZnk6PljXpo2ZaIqWKAr0sycuFec/DotehVmtnIYqIBm69dPwPWxg1K5lqoSG8dVM7dUYUKYUU6GXF4V0w5Q7Yugja3Qq9/uVcBC3G8WZazWqF0+/8GJ6+qjnVQjUVUaQ0UqCXBVsWOWGelQ7XvA3nDy72JRnZubwydz3lgw0j+rRQMy0RP6CLooHM5YKFr8P4q6FCONz1rVthvuC3PXQfvYDxS7aQk2fVTEvET2iEHqgy98OMe+G3L6HltdD3v06on8ahzBxGzU5myk+pNIhymmldGK9mWiL+QoEeiLb/DJNuhcM7oNcr0P4ut3qx7M3I5ovVO7ivU0Me7KpmWiL+RoEeSKyFFWPhyyegck231vrcfTiLxFVp3HlZgz+aaVVX/xURv6RADxTZR+Dzv8KaKdDoSug/BkJPfbrEWsvUn7czalYyR3Py6Nq8JvUjwxTmIn5MgR4Idq+DSbfAvt+hy1Nw6d8h6NTXu1P2Z/Lk9NUs/H0vCfWq89J1aqYlEggU6P4uaZIzMg8JgyEzoMEVp908N8/F4HeXciDjGKP6teSmDvUIUjMtkYCgQPdXOVkw9wlYMQ7iOuY31jr13Ztb9mYQGxFKueAgXh7gNNOqW139V0QCieah+6MDW2BcdyfML/lrfmOtosM8J8/Fm/M20H30gj+aaXVsGKkwFwlAGqH7m3VzYMY9YIFBn0Cz3qfcdM32Qzw2JYnkHen0aV2bq9q41xpXRPyTAt1f5OXCd6Ng8RtQ+zy4fjxE1D/l5u8v3sw/Z/9KRFgIb998AT1b1SrBYkXEFxTo/uDwzvzGWovhgtuh50tQvmKRmx5vptWyTlX6t43hqT4tqBpavoQLFhFfUKCXdpsXwJShcOwIXPsOnDeoyM2OZOfy8pfrCAkO4qmrWtC+fgTt6+u2fZGyRBdFSyuXCxa+BhP6QcWqcNd3pwzz+et302P0AiYu3YoFNdMSKaM0Qi+NMvc7Kwr9/hW0ug6u/neRjbUOZBxj1Oxkpv28nUbRlZlyT0cuqFfdBwWLSGmgQC9ttv8Ek25zGmv1fhUuvPOUjbUOZB7jq7W7eLBLI+7v0ogK5dRMS6Qsc+uUizGmpzFmvTFmgzFmeBHPP2yMSTbGJBljvjXG1PN8qQHOWvjxXRjbA7Bwx9wiuyTuTs9izIKNWGtpEFWZxY934eHuTRXmIlL8CN0YEwy8CVwJpALLjTGJ1trkAputBBKstZnGmHuBl4EbvFFwQMo+nN9Yayo07u5c/CzUWMtay+QVqYyancyxXBdXtqhF/cgwzWARkT+4c8qlPbDBWrsJwBjzKdAP+CPQrbXzCmy/FLjZk0UGtN2/wmdDYP9G6PoMXPLQSY21UvZn8sS01SzasJf29SN4qX9rNdMSkZO4E+gxQEqBx6lAh9NsPxT4oqgnjDHDgGEAcXFxbpYYwH75FGY9BCGV4ZaZUP/ykzY53kzrYGYO/7ymFTe2j1MzLREpkjuBXlR6FDkvzhhzM5AAFNnyz1o7BhgDkJCQUHbn1uVkwZePw08fQL1LnMZa4cePmo4AAAsvSURBVCfeybl5bwZx+c20XhlwHvVqhFKnWiXf1CsifsGdi6KpQGyBx3WBtMIbGWO6ASOAvtbabM+UF4D2b4axVzphfsnf4JbEE8I8J8/Ff7/9nR6jFzD+hy0AXNywhsJcRIrlzgh9OdDYGFMf2A4MAm4suIExpi3wDtDTWrvb41UGinWzYfq9zt88gz+Fpr1OeDop9SCPTUli3c7DXH1eHfqer2ZaIuK+YgPdWptrjHkAmAsEA+OstWuNMc8BK6y1icArQGVgsnGm2W2z1vb1Yt3+JS8Hvn0OfvgP1D4fBo6H6vEnbDJu0Wb+OTuZqPAKvHtLAle2qOmbWkXEb7l1Y5G1dg4wp9DXninweTcP1xU40nfAlNth2xJIGAo9XjihsdbxZlpt6lblhgtjGd6rOVUraSqiiJw53SnqTZvmw9Q74VgG9H8P2lz/x1OHs3J46Yt1VCgXzDNXtyAhPoKEeDXTEpGzp+Zc3uBywfevwMRroVJ1uGveCWE+b91uuo9ewCc/bqNcsFEzLRHxCI3QPS1zP0wbBhu+hlYD8htrVQZgf8Yxnvt8LTNWpdGkZmX+76aOtI1TMy0R8QwFuielroDJt8GRXdDnNeeceYFeLIeO5vDtr7v5a9fG3N+5ESHl9AeSiHiOAt0TjjfWmvskhNd2GmvFtANg56EsZqzazt2XN6B+ZBiLhnfRRU8R8QoF+rnKPgyJf4G106FJT7jmLQiNwFrLp8tTeGH2r+S4XPRsWYv4yDCFuYh4jQL9XOxKhkm35DfW+odz52dQEFv3ZTB86mqWbNrHRQ0ieKl/G+LVTEtEvEyBfrZWfeI01qoQ7ty+X/8ywGmmdeO7yzh0NIcXrm3NoAtj1UxLREqEAv1M5WTBF4/Bz+Oh3qUwYCyE12LjniPUy2+m9dpAp5lW7arqvyIiJUfTLM7E/k0wtpsT5pc+DLfM5FilaN745jd6vrGACUu2AnBRgxoKcxEpcRqhu+vXWTDjPmca4uDPoGlPVqUc5PEpSazfdZh+59fhmrYxvq5SRMowBXpx8nLgm5Gw5H9Qpy1cPx6q12Psos08PzuZ6PCKjL01ga7N1UxLRHxLgX466Wkw+XZIWQoX3gk9XsAGh2CA82OrMqh9HMN7NaNKRU1FFBHfU6CfysZ5TmOtnKNw3VjSG/fjxcR1VCwfxD+ubskF9SK4oJ6aaYlI6aGLooW5XPD9y05jrbBIGDaPb4Iv48rXv+ez5dsIKRekZloiUipphF5Qxj6Ydhds/BZaD2Rf53/x7NytJP6ygWa1whkzJIHzYqv5ukoRkSIp0I9LWQ6Tb4WMPXDVaLjgdg7vy2Te+t081K0J93ZqqGZaIlKqKdCthWVvw1dPQZU67Bn4OZPSIrkPiI8MY/HwLrroKSJ+oWwHelY6JD4AyTOxTXoyOfYpnvs4jTzXQfq0rk18ZJjCXET8RtkN9F1r4bMhcGAL+zuO4L5Nl7B09jYuaVSDF69tQ1yNUF9XKCJyRspmoK/6GGY9DBWrkDtkJldPyiE96wgvX9eG6xPqYoyaaYmI/ylbgZ5zFOY8CisnkhnTkZCB4yhXtTajb9hPvRqh1KxS0dcVioictbIzbWPfRnjvSlg5kWV1b6ft5vsYvzoLgPb1IxTmIuL3ysYIPTkRZt5PrjX8o9LTfLShOf3bxtBfzbREJIAEdqAXaKy1O7wl/fcOw1Ullvdvb03nptG+rk5ExKMCN9APbYcpt0PKMmg/jNRmD9MpaS+P92xGuKYiikgACsxA3/gdril3kpOdycz4ZxnY+2+0A9o1qO3rykREvCawLoq68mD+S9iJ/dl8NJSrskaxpVZPNdMSkTIhcEboGXs5NnkoIVvmMy3vUj6s8TdGX9+eVjFVfV2ZiEiJCIxA37YMJt9G+cx9PMswIjsPY9IVDSkfHFh/gIiInI5/B7q1HJz3H8IXPktQ1bqYoV/x9xqtqFzBvw9LRORsuDWENcb0NMasN8ZsMMYML+L5CsaYz/KfX2aMifd0oYW5Mg+y9e0BVFvwDPNcbUm5/kuoc77CXETKrGID3RgTDLwJ9AJaAIONMS0KbTYUOGCtbQSMBv7l6UIL2rXwfY680oqYnd/ySdU7afpgInExdby5SxGRUs+dEXp7YIO1dpO19hjwKdCv0Db9gPH5n08BuhovdbjKXfkJ0d/+jXB7GBNcnkHXDSS2Rpg3diUi4lfcCfQYIKXA49T8rxW5jbU2FzgE1Cj8RsaYYcaYFcaYFXv27DmrgssdTgMMBgi2eZiti87qfUREAo07gV7USLvwxG53tsFaO8Zam2CtTYiKinKnvpPVvwxTriKYYAgOgfjLzu59REQCjDtXEFOB2AKP6wJpp9gm1RhTDqgK7PdIhYXFtodbE2HLQifMY9t7ZTciIv7GnUBfDjQ2xtQHtgODgBsLbZMI3AosAQYA31lv3p4Z215BLiJSSLGBbq3NNcY8AMwFgoFx1tq1xpjngBXW2kRgLDDRGLMBZ2Q+yJtFi4jIydyatG2tnQPMKfS1Zwp8ngVc79nSRETkTOjeeBGRAKFAFxEJEAp0EZEAoUAXEQkQxleLPxhj9gBbz/LlkcBeD5bjD3TMZYOOuWw4l2OuZ60t8s5MnwX6uTDGrLDWJvi6jpKkYy4bdMxlg7eOWadcREQChAJdRCRA+Gugj/F1AT6gYy4bdMxlg1eO2S/PoYuIyMn8dYQuIiKFKNBFRAJEqQ700rg4tbe5ccwPG2OSjTFJxphvjTH1fFGnJxV3zAW2G2CMscYYv5/i5s4xG2MG5n+v1xpjPi7pGj3NjZ/tOGPMPGPMyvyf796+qNNTjDHjjDG7jTFrTvG8Mcb8J//fI8kY0+6cd2qtLZUfOK16NwINgBDgF6BFoW3uA97O/3wQ8Jmv6y6BY+4MhOZ/fm9ZOOb87cKBBcBSIMHXdZfA97kxsBKonv842td1l8AxjwHuzf+8BbDF13Wf4zFfDrQD1pzi+d7AFzgrvl0ELDvXfZbmEXqpWpy6hBR7zNbaedbazPyHS3FWkPJn7nyfAUYBLwNZJVmcl7hzzHcBb1prDwBYa3eXcI2e5s4xW6BK/udVOXllNL9irV3A6Vdu6wdMsI6lQDVjTO1z2WdpDnSPLU7tR9w55oKG4vwf3p8Ve8zGmLZArLV2VkkW5kXufJ+bAE2MMYuNMUuNMT1LrDrvcOeYRwI3G2NScdZf+EvJlOYzZ/r7Xiy3FrjwEY8tTu1H3D4eY8zNQAJwhVcr8r7THrMxJggYDdxWUgWVAHe+z+VwTrt0wvkrbKExppW19qCXa/MWd455MPCBtfY1Y8zFOKugtbLWurxfnk94PL9K8wj9TBanxuuLU5cMd44ZY0w3YATQ11qbXUK1eUtxxxwOtALmG2O24JxrTPTzC6Pu/mzPtNbmWGs3A+txAt5fuXPMQ4FJANbaJUBFnCZWgcqt3/czUZoD/Y/FqY0xITgXPRMLbXN8cWooicWpva/YY84//fAOTpj7+3lVKOaYrbWHrLWR1tp4a208znWDvtbaFb4p1yPc+dmegXMBHGNMJM4pmE0lWqVnuXPM24CuAMaY5jiBvqdEqyxZicAt+bNdLgIOWWt3nNM7+vpKcDFXiXsDv+FcHR+R/7XncH6hwfmGTwY2AD8CDXxdcwkc8zfALmBV/keir2v29jEX2nY+fj7Lxc3vswFeB5KB1cAgX9dcAsfcAliMMwNmFdDd1zWf4/F+AuwAcnBG40OBe4B7CnyP38z/91jtiZ9r3fovIhIgSvMpFxEROQMKdBGRAKFAFxEJEAp0EZEAoUAXEQkQCnQRkQChQBcRCRD/D5gJndC8sKIRAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "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": [
+    "new_predictions = np.transpose(softmax(new_logits, axis=1))\n",
+    "for i in range(10):\n",
+    "    fop, mpv = calibration_curve(y_true[i], new_predictions[i])\n",
+    "    plt.plot([0, 1], [0, 1], linestyle='--')\n",
+    "    plt.plot(mpv, fop, marker='.')\n",
+    "    plt.show() "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "calibr.MatrixScaling()\n",
+    "new_logits = calibr.matrix_scaling_logits(test_logits).detach().numpy()\n",
+    "calibr.compute_ece(15, new_logits, y_test.to_numpy(), len(y_test))"
+   ]
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+    "calibr.VectorScaling()\n",
+    "new_logits = calibr.vector_scaling_logits(test_logits).detach().numpy()\n",
+    "calibr.compute_ece(15, new_logits, y_test.to_numpy(), len(y_test))"
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diff --git a/examples/calibrator.py b/examples/calibrator.py
new file mode 100644
index 0000000..03d038d
--- /dev/null
+++ b/examples/calibrator.py
@@ -0,0 +1,211 @@
+import sklearn
+import numpy as np
+
+import math
+from torch.nn import functional as f
+import torch
+from torch import nn, optim
+import math
+from scipy.special import softmax
+
+
+class Calibrator():
+    def __init__(self, logits, labels):
+        self.temperature = torch.ones(1, requires_grad=True)
+        self.logits = logits
+        self.labels = labels
+        self.W = torch.diag(torch.ones(logits.shape[1]))
+        self.W.requires_grad_()
+        self.b = torch.zeros(logits.shape[1], requires_grad=True)
+        self.W_diag = torch.cat((torch.ones(logits.shape[1]), torch.zeros(logits.shape[1])), dim=0)
+        self.W_diag.requires_grad_()
+
+    def split_into_bins(self, n_bins, logits, labels):
+        bins = []
+        true_labels_for_bins = []
+
+        for i in range(n_bins):
+            bins.append([])
+            true_labels_for_bins.append([])
+
+        for j in range(len(labels)):
+            max_p = max(softmax(logits[j]))
+            for i in range(n_bins):
+                if i / n_bins < max_p and max_p <= (i + 1) / n_bins:
+                    bins[i].append((logits[j]))
+                    true_labels_for_bins[i].append(labels[j])
+        return np.array(bins), np.array(true_labels_for_bins)
+
+    def compute_ece(self, n_bins, logits, labels, len_dataset):
+        bins, true_labels_for_bins = self.split_into_bins(n_bins, logits, labels)
+        bins = list(filter(None, bins))
+        true_labels_for_bins = list(filter(None, true_labels_for_bins))
+        ece = torch.zeros(1)
+        for i in range(len(bins)):
+            softmaxes = f.softmax(torch.from_numpy(np.array(bins[i])), dim=1)
+            confidences, predictions = torch.max(softmaxes, dim=1)
+            accuracy = sklearn.metrics.accuracy_score(true_labels_for_bins[i], predictions)
+            confidence = torch.sum(confidences) / len(bins[i])
+            ece += len(bins[i]) * torch.abs(accuracy - confidence) / len_dataset
+        return ece
+
+    def split_into_classes(self, dataset, column_label, logits):
+        by_column = dataset.groupby(column_label)
+        datasets = {}
+        class_logits = []
+        dict_class_logits = {}
+        n_classes = len(set(dataset[column_label]))
+        for i in range(n_classes):
+            class_logits.append([])
+        for groups, data in by_column:
+            datasets[groups] = data
+        for ind, label in enumerate(dataset[column_label].to_numpy()):
+            for i in range(n_classes):
+                if label == i:
+                    class_logits[i].append(logits[ind])
+        for i in range(n_classes):
+            dict_class_logits[i] = class_logits[i]
+        return datasets, dict_class_logits
+
+    def compute_sce(self, nbins, column_label, logits, dataset):
+        ece_values_for_each_class = []
+        datasets, dict_class_logits = self.split_into_classes(dataset, column_label, logits)
+        for item in datasets.keys():
+            ece_values_for_each_class.append(
+                self.compute_ece(nbins, dict_class_logits[item], datasets[item][column_label].to_numpy(), len(dataset)))
+        return sum(ece_values_for_each_class) / len(datasets.keys())
+
+    def SplitIntoRanges(self, R, logits, labels):
+        N = len(logits)
+        bins = []
+        true_labels = []
+        for i in range(R):
+            bins.append([])
+            true_labels.append([])
+        for j in range(R):
+            for i in range(j * math.floor(N / R), (j + 1) * math.floor(N / R)):
+                bins[j].append(logits[i])
+                true_labels[j].append(labels[i])
+        return np.array(bins), np.array(true_labels)
+
+    def ComputeAce(self, R, dataset, target, logits):
+        datasets, dict_class_logits = self.split_into_classes(dataset, target, logits)
+        summa = 0
+        for dataset in datasets.keys():
+            data = datasets[dataset]
+            class_labels = data[target].to_numpy()
+            class_logits = dict_class_logits[dataset]
+            bins, true_labels = self.SplitIntoRanges(R, class_logits, class_labels)
+            for binn, bin_labels in zip(bins, true_labels):
+                softmaxes = f.softmax(torch.from_numpy(binn), dim=1)
+                accuracy = sklearn.metrics.accuracy_score(torch.from_numpy(bin_labels), np.argmax(softmaxes, axis=1))
+                conf_array = torch.max(softmaxes, dim=1)[0]
+                confidence = torch.sum(conf_array) / len(conf_array)
+                substraction = abs(accuracy - confidence)
+                summa += substraction
+        ACE = summa / (len(datasets.keys()) * R)
+        return ACE
+
+    def ChooseData(self, threshold, dataset, logits):
+        arr = torch.max(f.softmax(torch.from_numpy(logits), dim=1), dim=1)[0]
+        arr.numpy()
+        arr_with_indices = list(enumerate(arr))
+        arr_with_indices.sort(key=lambda x: x[1])
+        thr_array = []
+        for pair in arr_with_indices:
+            if pair[1] > threshold:
+                thr_array.append(pair)
+        indices = []
+        for pair in thr_array:
+            indices.append(pair[0])
+        chosen_data = dataset.iloc[indices]
+        chosen_logits = logits[indices]
+        return chosen_data, chosen_logits
+
+    def ComputeTace(self, threshold, dataset, logits, R, target):
+        chosen_data, chosen_logits = self.ChooseData(threshold, dataset, logits)
+        return self.ComputeAce(R, chosen_data, target, chosen_logits)
+
+    def NumberOfClasses(self, dataset, target):
+        by_column = dataset.groupby(target)
+        datasets = {}
+        for groups, data in by_column:
+            datasets[groups] = data
+        return len(datasets)
+
+    def matrix_scaling_logits(self, logits):
+        self.b.unsqueeze(0).expand(logits.shape[0], -1)
+        return torch.mm(torch.from_numpy(logits), self.W) + self.b
+
+    def vector_scaling_logits(self, logits):
+        W = torch.diag(self.W_diag[:logits.shape[1]])
+        b = self.W_diag[logits.shape[1]:]
+        b = b.unsqueeze(0).expand(logits.shape[0], -1)
+        return torch.mm(torch.from_numpy(logits), W) + b
+
+    def scale_logits_with_temperature(self, logits):
+        self.temperature.unsqueeze(1).expand(logits.shape[0], logits.shape[1])
+        return torch.true_divide(torch.from_numpy(logits), self.temperature)
+
+    def TemperatureScaling(self):
+        nll = nn.CrossEntropyLoss()
+        optimizer = optim.LBFGS([self.temperature], lr=0.0001, max_iter=500)
+
+        def eval():
+            loss = nll(self.scale_logits_with_temperature(self.logits), torch.from_numpy(np.array(self.labels)))
+            loss.backward()
+            return loss
+
+        optimizer.step(eval)
+        return self
+
+    def MatrixScaling(self):
+
+        nll = nn.CrossEntropyLoss()
+        optimizer = optim.LBFGS([self.W, self.b], lr=0.0001, max_iter=1000)
+
+        def eval():
+            loss = nll(self.matrix_scaling_logits(self.logits), torch.from_numpy(np.array(self.labels)))
+            loss.backward()
+            return loss
+
+        optimizer.step(eval)
+        return self
+
+    def VectorScaling(self):
+        nll = nn.CrossEntropyLoss()
+        optimizer = optim.LBFGS([self.W_diag], lr=0.000001, max_iter=9000)
+
+        def eval():
+            loss = nll(self.vector_scaling_logits(self.logits), torch.from_numpy(np.array(self.labels)))
+            loss.backward()
+            return loss
+
+        optimizer.step(eval)
+        return self
+
+
+def binary_histogram_binning(num_bins, probs, labels, probs_to_calibrate):
+    bins = np.linspace(0, 1, num=num_bins)
+    indexes_list = np.digitize(probs, bins) - 1
+    theta = np.zeros(num_bins)
+    for i in range(len(bins)):
+        binn = (indexes_list == i)
+        binn_len = np.sum(binn)
+        if binn_len != 0:
+            theta[i] = np.sum(labels[binn]) / binn_len
+        else:
+            theta[i] = bins[i]
+    return list(map(lambda x: theta[np.digitize(x, bins) - 1], probs_to_calibrate))
+
+
+def multiclass_histogram_binning(num_bins, logits, labels, logits_to_calibrate):
+    probs = softmax(logits, axis=1)
+    probs_to_calibrate = softmax(logits_to_calibrate, axis=1)
+    binning_res = []
+    for k in range(np.shape(probs)[1]):
+        binning_res.append(binary_histogram_binning(num_bins, probs[:, k], labels == k, probs_to_calibrate[:, k]))
+    binning_res = np.vstack(binning_res).T
+    cal_confs = binning_res / (np.sum(binning_res, axis=1)[:, None])
+    return cal_confs
+

From a8a8e4910c57270f1049c6d31b5fff35f2ead001 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=D0=9C=D0=B8=D1=85=D0=B0=D0=B8=D0=BB=20=D0=A2=D0=B5=D1=80?=
 =?UTF-8?q?=D0=B5=D1=88=D0=BA=D0=B8=D0=BD?= <tereshkin.ma@phystech.edu>
Date: Sun, 6 Sep 2020 16:58:10 +0300
Subject: [PATCH 2/8] Change names of methods

---
 alpaca/calibrator.py               | 232 +++++++++++++++++++++++++++++
 examples/calibration_example.ipynb |  25 +++-
 2 files changed, 254 insertions(+), 3 deletions(-)
 create mode 100644 alpaca/calibrator.py

diff --git a/alpaca/calibrator.py b/alpaca/calibrator.py
new file mode 100644
index 0000000..2bf5328
--- /dev/null
+++ b/alpaca/calibrator.py
@@ -0,0 +1,232 @@
+from sklearn.metrics import accuracy_score
+import numpy as np
+import math
+from torch.nn import functional as f
+import torch
+from torch import nn, optim
+from scipy.special import softmax
+import pandas as pd
+
+
+def _split_into_bins(n_bins, probs, labels):
+    bins = []
+    true_labels_for_bins = []
+
+    for i in range(n_bins):
+        bins.append([])
+        true_labels_for_bins.append([])
+
+    for j in range(len(labels)):
+        max_p = max(probs[j])
+        for i in range(n_bins):
+            if i / n_bins < max_p and max_p <= (i + 1) / n_bins:
+                bins[i].append((probs[j]))
+                true_labels_for_bins[i].append(labels[j])
+    return np.array(bins, dtype=object), np.array(true_labels_for_bins, dtype=object)
+
+
+def compute_ece(n_bins, probs, labels, len_dataset):
+    bins, true_labels_for_bins = _split_into_bins(n_bins, probs, labels)
+    bins = list(filter(None, bins))
+    true_labels_for_bins = list(filter(None, true_labels_for_bins))
+    ece = torch.zeros(1)
+    for i in range(len(bins)):
+        softmaxes = torch.from_numpy(np.array(bins[i]))
+        confidences, predictions = torch.max(softmaxes, dim=1)
+        accuracy = accuracy_score(true_labels_for_bins[i], predictions)
+        confidence = torch.sum(confidences) / len(bins[i])
+        ece += len(bins[i]) * torch.abs(accuracy - confidence) / len_dataset
+    return ece
+
+
+def _split_into_classes(labels, probs):
+    class_probs = []
+    dict_class_probs = {}
+    n_classes = np.shape(probs)[1]
+    for i in range(n_classes):
+        class_probs.append([])
+    for ind, label in enumerate(labels):
+        for i in range(n_classes):
+            if label == i:
+                class_probs[i].append(probs[ind])
+    for i in range(n_classes):
+        dict_class_probs[i] = class_probs[i]
+    return dict_class_probs
+
+
+def compute_sce(nbins, probs, labels):
+    ece_values_for_each_class = []
+    dict_class_probs = _split_into_classes(labels, probs)
+    for item in dict_class_probs.keys():
+        ece_values_for_each_class.append(
+            compute_ece(nbins, dict_class_probs[item], np.array([item] * np.shape(dict_class_probs[item])[0]),
+                        len(labels)))
+    return sum(ece_values_for_each_class) / len(dict_class_probs.keys())
+
+
+def _split_into_ranges(R, probs, labels):
+    N = len(probs)
+    bins = []
+    true_labels = []
+    for i in range(R):
+        bins.append([])
+        true_labels.append([])
+    for j in range(R):
+        for i in range(j * math.floor(N / R), (j + 1) * math.floor(N / R)):
+            bins[j].append(probs[i])
+            true_labels[j].append(labels[i])
+    return np.array(bins, dtype=object), np.array(true_labels, dtype=object)
+
+
+def compute_ace(R, labels, probs):
+    dict_class_probs = _split_into_classes(labels, probs)
+    summa = 0
+    for item in dict_class_probs.keys():
+        class_labels = np.array([item] * np.shape(dict_class_probs[item])[0])
+        class_probs = dict_class_probs[item]
+        bins, true_labels = _split_into_ranges(R, class_probs, class_labels)
+        for binn, bin_labels in zip(bins, true_labels):
+            conf_array, predictions = torch.max(torch.from_numpy(binn), dim=1)
+            accuracy = accuracy_score(bin_labels, predictions.numpy())
+            confidence = torch.sum(conf_array) / len(conf_array)
+            substraction = abs(accuracy - confidence)
+            summa += substraction
+    ACE = summa / (len(dict_class_probs.keys()) * R)
+    return ACE
+
+
+def _choose_data(threshold, labels, probs):
+    arr = torch.max(torch.from_numpy(np.array(probs)), dim=1)[0]
+    arr.numpy()
+    arr_with_indices = list(enumerate(arr))
+    arr_with_indices.sort(key=lambda x: x[1])
+    thr_array = []
+    for pair in arr_with_indices:
+        if pair[1] > threshold:
+            thr_array.append(pair)
+    indices = []
+    for pair in thr_array:
+        indices.append(pair[0])
+    chosen_labels = labels[indices]
+    chosen_probs = probs[indices]
+    return chosen_labels, chosen_probs
+
+
+def compute_tace(threshold, labels, probs, R):
+    if isinstance(labels, pd.DataFrame) or isinstance(labels, pd.Series):
+        labels = labels.to_numpy()
+    chosen_labels, chosen_probs = _choose_data(threshold, labels, probs)
+    return compute_ace(R, chosen_labels, chosen_probs)
+
+
+class ModelWithTempScaling(nn.Module):
+
+    def __init__(self, model, logits, labels):
+        super(ModelWithTempScaling, self).__init__()
+        self.model = model
+        self.temperature = nn.Parameter(torch.ones(1))
+        self.logits = logits
+        self.labels = labels
+
+    def forward(self, input):
+        logits = self.model(input)
+        return torch.true_divide(logits, self.temperature)
+
+    def scaling(self, lr=0.01, max_iter=50):
+        nll = nn.CrossEntropyLoss()
+        optimizer = optim.LBFGS([self.temperature], lr=lr, max_iter=max_iter)
+
+        def eval():
+            loss = nll(torch.true_divide(self.logits, self.temperature), self.labels)
+            loss.backward()
+            return loss
+
+        optimizer.step(eval)
+        return self
+
+
+class ModelWithVectScaling(nn.Module):
+    def __init__(self, model, logits, labels):
+        super(ModelWithVectScaling, self).__init__()
+        self.model = model
+        self.logits = logits.float()
+        self.labels = labels
+        self.W_and_b = nn.Parameter(
+            torch.cat((torch.ones(logits.shape[1]), torch.zeros(logits.shape[1])), dim=0))
+
+    def forward(self, input):
+        logits = self.model(input)
+        return self.scaling_logits(logits)
+
+    def scaling_logits(self, logits):
+        W = torch.diag(self.W_and_b[:logits.shape[1]])
+        b = self.W_and_b[logits.shape[1]:]
+        b = b.unsqueeze(0).expand(logits.shape[0], -1)
+        return torch.mm(logits, W) + b
+
+    def scaling(self, lr=0.00001, max_iter=3500):
+        nll = nn.CrossEntropyLoss()
+        optimizer = optim.LBFGS([self.W_and_b], lr=lr, max_iter=max_iter)
+
+        def eval():
+            loss = nll(self.vector_scaling_logits(self.logits), self.labels)
+            loss.backward()
+            return loss
+
+        optimizer.step(eval)
+        return self
+
+
+class ModelWithMatrScaling(nn.Module):
+    def __init__(self, model, logits, labels):
+        super(ModelWithMatrScaling, self).__init__()
+        self.model = model
+        self.logits = logits.float()
+        self.labels = labels
+        self.W = nn.Parameter(torch.diag(torch.ones(logits.shape[1])))
+        self.b = nn.Parameter(torch.zeros(logits.shape[1]))
+
+    def forward(self, input):
+        logits = self.model(input)
+        return self.scaling_logits(logits)
+
+    def scaling_logits(self, logits):
+        self.b.unsqueeze(0).expand(logits.shape[0], -1)
+        return torch.mm(logits, self.W) + self.b
+
+    def scaling(self, lr=0.001, max_iter=100):
+        nll = nn.CrossEntropyLoss()
+        optimizer = optim.LBFGS([self.W, self.b], lr=lr, max_iter=max_iter)
+
+        def eval():
+            loss = nll(self.matrix_scaling_logits(self.logits), self.labels)
+            loss.backward()
+            return loss
+
+        optimizer.step(eval)
+        return self
+
+
+def binary_histogram_binning(num_bins, probs, labels, probs_to_calibrate):
+    bins = np.linspace(0, 1, num=num_bins)
+    indexes_list = np.digitize(probs, bins) - 1
+    theta = np.zeros(num_bins)
+    for i in range(len(bins)):
+        binn = (indexes_list == i)
+        binn_len = np.sum(binn)
+        if binn_len != 0:
+            theta[i] = np.sum(labels[binn]) / binn_len
+        else:
+            theta[i] = bins[i]
+    return list(map(lambda x: theta[np.digitize(x, bins) - 1], probs_to_calibrate))
+
+
+def multiclass_histogram_binning(num_bins, logits, labels, logits_to_calibrate):
+    probs = softmax(logits, axis=1)
+    probs_to_calibrate = softmax(logits_to_calibrate, axis=1)
+    binning_res = []
+    for k in range(np.shape(probs)[1]):
+        binning_res.append(binary_histogram_binning(num_bins, probs[:, k], labels == k, probs_to_calibrate[:, k]))
+    binning_res = np.vstack(binning_res).T
+    cal_confs = binning_res / (np.sum(binning_res, axis=1)[:, None])
+    return cal_confs
diff --git a/examples/calibration_example.ipynb b/examples/calibration_example.ipynb
index f9e6227..3dc355d 100644
--- a/examples/calibration_example.ipynb
+++ b/examples/calibration_example.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 50,
+   "execution_count": 1,
    "metadata": {
     "colab": {
      "base_uri": "https://localhost:8080/",
@@ -94,7 +94,26 @@
     "id": "ygJyUrpkB2rR",
     "outputId": "2eb7ae89-c6a2-454f-8f91-ca05c6a6cf3c"
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "ename": "FileNotFoundError",
+     "evalue": "[Errno 2] File b'mnist_test.csv' does not exist: b'mnist_test.csv'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mFileNotFoundError\u001b[0m                         Traceback (most recent call last)",
+      "\u001b[0;32m<ipython-input-2-56fc56744261>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mtest_data\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mread_csv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'mnist_test.csv'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mtrain_data\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mread_csv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'mnist_train.csv'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/PycharmProjects/untitled1/venv/lib/python3.6/site-packages/pandas/io/parsers.py\u001b[0m in \u001b[0;36mparser_f\u001b[0;34m(filepath_or_buffer, sep, delimiter, header, names, index_col, usecols, squeeze, prefix, mangle_dupe_cols, dtype, engine, converters, true_values, false_values, skipinitialspace, skiprows, skipfooter, nrows, na_values, keep_default_na, na_filter, verbose, skip_blank_lines, parse_dates, infer_datetime_format, keep_date_col, date_parser, dayfirst, cache_dates, iterator, chunksize, compression, thousands, decimal, lineterminator, quotechar, quoting, doublequote, escapechar, comment, encoding, dialect, error_bad_lines, warn_bad_lines, delim_whitespace, low_memory, memory_map, float_precision)\u001b[0m\n\u001b[1;32m    683\u001b[0m         )\n\u001b[1;32m    684\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 685\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0m_read\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfilepath_or_buffer\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkwds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    686\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    687\u001b[0m     \u001b[0mparser_f\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__name__\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/PycharmProjects/untitled1/venv/lib/python3.6/site-packages/pandas/io/parsers.py\u001b[0m in \u001b[0;36m_read\u001b[0;34m(filepath_or_buffer, kwds)\u001b[0m\n\u001b[1;32m    455\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    456\u001b[0m     \u001b[0;31m# Create the parser.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 457\u001b[0;31m     \u001b[0mparser\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mTextFileReader\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfp_or_buf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    458\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    459\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mchunksize\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0miterator\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/PycharmProjects/untitled1/venv/lib/python3.6/site-packages/pandas/io/parsers.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, f, engine, **kwds)\u001b[0m\n\u001b[1;32m    893\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0moptions\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"has_index_names\"\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mkwds\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"has_index_names\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    894\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 895\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_make_engine\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mengine\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    896\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    897\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mclose\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/PycharmProjects/untitled1/venv/lib/python3.6/site-packages/pandas/io/parsers.py\u001b[0m in \u001b[0;36m_make_engine\u001b[0;34m(self, engine)\u001b[0m\n\u001b[1;32m   1133\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m_make_engine\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mengine\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"c\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1134\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mengine\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m\"c\"\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1135\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_engine\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mCParserWrapper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0moptions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1136\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1137\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mengine\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m\"python\"\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/PycharmProjects/untitled1/venv/lib/python3.6/site-packages/pandas/io/parsers.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, src, **kwds)\u001b[0m\n\u001b[1;32m   1915\u001b[0m         \u001b[0mkwds\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"usecols\"\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0musecols\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1916\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1917\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_reader\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mparsers\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mTextReader\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msrc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1918\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0munnamed_cols\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_reader\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0munnamed_cols\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1919\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32mpandas/_libs/parsers.pyx\u001b[0m in \u001b[0;36mpandas._libs.parsers.TextReader.__cinit__\u001b[0;34m()\u001b[0m\n",
+      "\u001b[0;32mpandas/_libs/parsers.pyx\u001b[0m in \u001b[0;36mpandas._libs.parsers.TextReader._setup_parser_source\u001b[0;34m()\u001b[0m\n",
+      "\u001b[0;31mFileNotFoundError\u001b[0m: [Errno 2] File b'mnist_test.csv' does not exist: b'mnist_test.csv'"
+     ]
+    }
+   ],
    "source": [
     "test_data = pd.read_csv('mnist_test.csv')\n",
     "train_data = pd.read_csv('mnist_train.csv')"
@@ -634,7 +653,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.6"
+   "version": "3.6.2"
   },
   "widgets": {
    "application/vnd.jupyter.widget-state+json": {

From e59f0df258abaae2ccd98f577cd15fe3bdf758af Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=D0=9C=D0=B8=D1=85=D0=B0=D0=B8=D0=BB=20=D0=A2=D0=B5=D1=80?=
 =?UTF-8?q?=D0=B5=D1=88=D0=BA=D0=B8=D0=BD?= <tereshkin.ma@phystech.edu>
Date: Sun, 6 Sep 2020 18:56:19 +0300
Subject: [PATCH 3/8] Add function "compute_errors"

---
 examples/calibration_example.ipynb | 726 +++++++++++++++--------------
 1 file changed, 384 insertions(+), 342 deletions(-)

diff --git a/examples/calibration_example.ipynb b/examples/calibration_example.ipynb
index 3dc355d..27fd811 100644
--- a/examples/calibration_example.ipynb
+++ b/examples/calibration_example.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 85,
    "metadata": {
     "colab": {
      "base_uri": "https://localhost:8080/",
@@ -19,14 +19,47 @@
     "import calibrator\n",
     "import numpy as np\n",
     "import pandas as pd\n",
-    "from sklearn.neural_network import MLPClassifier\n",
-    "from sklearn.calibration import calibration_curve\n",
-    "import matplotlib.pyplot as plt"
+    "from alpaca.dataloader.builder import build_dataset"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 86,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import sklearn\n",
+    "import math\n",
+    "from torch.nn import functional as f\n",
+    "import torch\n",
+    "from torch import nn, optim\n",
+    "from torch.utils.data import TensorDataset, DataLoader"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 87,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def compute_errors(n_bins, probs, labels, len_dataset, threshold):\n",
+    "    ece = calibrator.compute_ece(n_bins, probs, labels, len_dataset)\n",
+    "    sce = calibrator.compute_sce(n_bins, probs, labels)\n",
+    "    ace = calibrator.compute_ace(n_bins, labels, probs)\n",
+    "    tace = calibrator.compute_tace(threshold, labels, probs, n_bins)\n",
+    "    errors = {\n",
+    "        'ece' : ece,\n",
+    "        'sce' : sce,\n",
+    "        'ace' : ace,\n",
+    "        'tace' : tace\n",
+    "    }\n",
+    "    for error in errors.items():\n",
+    "        print(str(error[0]), ' = ', error[1])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 74,
    "metadata": {
     "colab": {
      "base_uri": "https://localhost:8080/",
@@ -94,54 +127,81 @@
     "id": "ygJyUrpkB2rR",
     "outputId": "2eb7ae89-c6a2-454f-8f91-ca05c6a6cf3c"
    },
+   "outputs": [],
+   "source": [
+    "mnist = build_dataset('mnist', val_size=10_000)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 75,
+   "metadata": {},
    "outputs": [
     {
-     "ename": "FileNotFoundError",
-     "evalue": "[Errno 2] File b'mnist_test.csv' does not exist: b'mnist_test.csv'",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mFileNotFoundError\u001b[0m                         Traceback (most recent call last)",
-      "\u001b[0;32m<ipython-input-2-56fc56744261>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mtest_data\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mread_csv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'mnist_test.csv'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mtrain_data\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mread_csv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'mnist_train.csv'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m~/PycharmProjects/untitled1/venv/lib/python3.6/site-packages/pandas/io/parsers.py\u001b[0m in \u001b[0;36mparser_f\u001b[0;34m(filepath_or_buffer, sep, delimiter, header, names, index_col, usecols, squeeze, prefix, mangle_dupe_cols, dtype, engine, converters, true_values, false_values, skipinitialspace, skiprows, skipfooter, nrows, na_values, keep_default_na, na_filter, verbose, skip_blank_lines, parse_dates, infer_datetime_format, keep_date_col, date_parser, dayfirst, cache_dates, iterator, chunksize, compression, thousands, decimal, lineterminator, quotechar, quoting, doublequote, escapechar, comment, encoding, dialect, error_bad_lines, warn_bad_lines, delim_whitespace, low_memory, memory_map, float_precision)\u001b[0m\n\u001b[1;32m    683\u001b[0m         )\n\u001b[1;32m    684\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 685\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0m_read\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfilepath_or_buffer\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkwds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    686\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    687\u001b[0m     \u001b[0mparser_f\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__name__\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m~/PycharmProjects/untitled1/venv/lib/python3.6/site-packages/pandas/io/parsers.py\u001b[0m in \u001b[0;36m_read\u001b[0;34m(filepath_or_buffer, kwds)\u001b[0m\n\u001b[1;32m    455\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    456\u001b[0m     \u001b[0;31m# Create the parser.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 457\u001b[0;31m     \u001b[0mparser\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mTextFileReader\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfp_or_buf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    458\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    459\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mchunksize\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0miterator\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m~/PycharmProjects/untitled1/venv/lib/python3.6/site-packages/pandas/io/parsers.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, f, engine, **kwds)\u001b[0m\n\u001b[1;32m    893\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0moptions\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"has_index_names\"\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mkwds\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"has_index_names\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    894\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 895\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_make_engine\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mengine\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    896\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    897\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mclose\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m~/PycharmProjects/untitled1/venv/lib/python3.6/site-packages/pandas/io/parsers.py\u001b[0m in \u001b[0;36m_make_engine\u001b[0;34m(self, engine)\u001b[0m\n\u001b[1;32m   1133\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m_make_engine\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mengine\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"c\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1134\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mengine\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m\"c\"\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1135\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_engine\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mCParserWrapper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0moptions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1136\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1137\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mengine\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m\"python\"\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m~/PycharmProjects/untitled1/venv/lib/python3.6/site-packages/pandas/io/parsers.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, src, **kwds)\u001b[0m\n\u001b[1;32m   1915\u001b[0m         \u001b[0mkwds\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"usecols\"\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0musecols\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1916\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1917\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_reader\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mparsers\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mTextReader\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msrc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1918\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0munnamed_cols\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_reader\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0munnamed_cols\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1919\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32mpandas/_libs/parsers.pyx\u001b[0m in \u001b[0;36mpandas._libs.parsers.TextReader.__cinit__\u001b[0;34m()\u001b[0m\n",
-      "\u001b[0;32mpandas/_libs/parsers.pyx\u001b[0m in \u001b[0;36mpandas._libs.parsers.TextReader._setup_parser_source\u001b[0;34m()\u001b[0m\n",
-      "\u001b[0;31mFileNotFoundError\u001b[0m: [Errno 2] File b'mnist_test.csv' does not exist: b'mnist_test.csv'"
-     ]
+     "data": {
+      "text/plain": [
+       "(10000, 784)"
+      ]
+     },
+     "execution_count": 75,
+     "metadata": {},
+     "output_type": "execute_result"
     }
    ],
    "source": [
-    "test_data = pd.read_csv('mnist_test.csv')\n",
-    "train_data = pd.read_csv('mnist_train.csv')"
+    "X_train, y_train = mnist.dataset('train')\n",
+    "X_val, y_val = mnist.dataset('val')\n",
+    "X_cal = X_train[48000:][:]\n",
+    "X_train = X_train[0:48000][:]\n",
+    "y_cal = y_train[48000:][:]\n",
+    "y_train = y_train[0:48000][:]\n",
+    "\n",
+    "x_shape = (-1, 1, 28, 28)\n",
+    "\n",
+    "train_ds = TensorDataset(torch.FloatTensor(X_train.reshape(x_shape)), torch.LongTensor(y_train))\n",
+    "val_ds = TensorDataset(torch.FloatTensor(X_val.reshape(x_shape)), torch.LongTensor(y_val))\n",
+    "train_loader = DataLoader(train_ds, batch_size=512)\n",
+    "val_loader = DataLoader(val_ds, batch_size=512)\n",
+    "cal_ds = TensorDataset(torch.FloatTensor(X_cal.reshape(x_shape)), torch.LongTensor(y_cal))\n",
+    "cal_loader = DataLoader(cal_ds, batch_size=512)\n",
+    "X_val.shape"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {
-    "colab": {},
-    "colab_type": "code",
-    "id": "I5XO9RDjB2rU"
-   },
+   "execution_count": 76,
+   "metadata": {},
    "outputs": [],
    "source": [
-    "y_test = test_data['label']\n",
-    "y_train = train_data['label'][0:48000]\n",
-    "X_test = test_data.drop(columns=['label'])\n",
-    "X_train = train_data.drop(columns=['label'])\n",
-    "X_train = X_train[0:48000][:]\n",
-    "cal = train_data[48000:][:]\n",
-    "y_cal = cal['label']\n",
-    "X_cal = cal.drop(columns=['label'])"
+    "class Net(nn.Module):   \n",
+    "    def __init__(self):\n",
+    "        super(Net, self).__init__()\n",
+    "\n",
+    "        self.cnn_layers = nn.Sequential(\n",
+    "            nn.Conv2d(1, 4, kernel_size=3, stride=1, padding=1),\n",
+    "            nn.BatchNorm2d(4),\n",
+    "            nn.ReLU(inplace=True),\n",
+    "            nn.MaxPool2d(kernel_size=2, stride=2),\n",
+    "            nn.Conv2d(4, 4, kernel_size=3, stride=1, padding=1),\n",
+    "            nn.BatchNorm2d(4),\n",
+    "            nn.ReLU(inplace=True),\n",
+    "            nn.MaxPool2d(kernel_size=2, stride=2),\n",
+    "        )\n",
+    "\n",
+    "        self.linear_layers = nn.Sequential(\n",
+    "            nn.Linear(4 * 7 * 7, 10)\n",
+    "        )\n",
+    "  \n",
+    "    def forward(self, x):\n",
+    "        x = self.cnn_layers(x)\n",
+    "        x = x.view(x.size(0), -1)\n",
+    "        x = self.linear_layers(x)\n",
+    "        return x"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 77,
    "metadata": {
     "colab": {
      "base_uri": "https://localhost:8080/",
@@ -151,483 +211,465 @@
     "id": "8qM2NebHB2ra",
     "outputId": "eaea1671-b680-489a-8cb6-68a734ab759e"
    },
+   "outputs": [],
+   "source": [
+    "model = Net()\n",
+    "criterion = nn.CrossEntropyLoss()\n",
+    "optimizer = torch.optim.Adam(model.parameters())"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 78,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "..............................................................................................\n",
+      "Train loss on last batch 0.5379677414894104\n",
+      "..............................................................................................\n",
+      "Train loss on last batch 0.3088064193725586\n",
+      "..............................................................................................\n",
+      "Train loss on last batch 0.22927790880203247\n",
+      "..............................................................................................\n",
+      "Train loss on last batch 0.18548454344272614\n",
+      "..............................................................................................\n",
+      "Train loss on last batch 0.15679685771465302\n",
+      "Accuracy 0.962890625\n"
+     ]
+    }
+   ],
+   "source": [
+    "for epoch in range(5):\n",
+    "    for x_batch, y_batch in train_loader: # Train for one epoch\n",
+    "        print('.', end='')\n",
+    "        prediction = model(x_batch)\n",
+    "        optimizer.zero_grad()\n",
+    "        loss = criterion(prediction, y_batch)\n",
+    "        loss.backward()\n",
+    "        optimizer.step()\n",
+    "    print('\\nTrain loss on last batch', loss.item())\n",
+    "\n",
+    "# Check accuracy\n",
+    "x_batch, y_batch = next(iter(val_loader))\n",
+    "\n",
+    "\n",
+    "class_preds = f.softmax(model(x_batch), dim=-1).detach().numpy()\n",
+    "predictions = np.argmax(class_preds, axis=-1)\n",
+    "print('Accuracy', accuracy_score(predictions, y_batch))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 88,
+   "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "MLPClassifier(activation='relu', alpha=0.0001, batch_size='auto', beta_1=0.9,\n",
-       "              beta_2=0.999, early_stopping=False, epsilon=1e-08,\n",
-       "              hidden_layer_sizes=(100, 100), learning_rate='constant',\n",
-       "              learning_rate_init=0.001, max_fun=15000, max_iter=300,\n",
-       "              momentum=0.9, n_iter_no_change=10, nesterovs_momentum=True,\n",
-       "              power_t=0.5, random_state=1, shuffle=True, solver='adam',\n",
-       "              tol=0.0001, validation_fraction=0.1, verbose=False,\n",
-       "              warm_start=False)"
+       "tensor([[-6.1167, -8.9871,  3.8799,  ..., -7.2181,  7.8800, -6.4360],\n",
+       "        [-0.1971,  4.4322, -0.6775,  ..., -2.8865,  2.0842, -4.1036],\n",
+       "        [-3.9227, -3.9793, -0.0458,  ..., -0.7269, -1.2891, -0.3848],\n",
+       "        ...,\n",
+       "        [-4.0691, -1.3082, -3.1546,  ..., -0.4103, -2.4649,  1.1635],\n",
+       "        [10.0700, -8.9821, -1.3832,  ..., -5.1656,  2.8142,  0.3769],\n",
+       "        [-7.6608, -3.4758, -6.1055,  ..., -0.1984,  0.0988,  6.5401]])"
       ]
      },
-     "execution_count": 5,
+     "execution_count": 88,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "clf = MLPClassifier((100, 100,), max_iter=300, random_state=1)\n",
-    "clf.fit(X_train, y_train)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {
-    "colab": {},
-    "colab_type": "code",
-    "id": "5hBUkdNCHyAs"
-   },
-   "outputs": [],
-   "source": [
-    "clf.out_activation_ = 'identity'\n",
-    "logits = clf.predict_proba(X_cal)"
+    "logits_list = []\n",
+    "labels_list = []\n",
+    "for x_batch, y_batch in cal_loader:\n",
+    "    logits_list.append(model(x_batch))\n",
+    "    labels_list.append(y_batch)\n",
+    "logits = torch.cat(logits_list)\n",
+    "labels = torch.cat(labels_list)\n",
+    "logits.detach_()\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 51,
-   "metadata": {
-    "colab": {},
-    "colab_type": "code",
-    "id": "0Qp6L3N8IC-c"
-   },
+   "execution_count": 89,
+   "metadata": {},
    "outputs": [],
    "source": [
-    "calibr = calibrator.Calibrator(logits, y_cal)"
+    "calibr = calibrator.ModelWithTempScaling(model, logits, labels)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 57,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/",
-     "height": 34
-    },
-    "colab_type": "code",
-    "id": "nkE0lL29Jo6T",
-    "outputId": "9e845720-4268-4709-ef4e-e7b0998f61f2"
-   },
+   "execution_count": 90,
+   "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "tensor([0.0244])"
+       "ModelWithTempScaling(\n",
+       "  (model): Net(\n",
+       "    (cnn_layers): Sequential(\n",
+       "      (0): Conv2d(1, 4, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))\n",
+       "      (1): BatchNorm2d(4, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
+       "      (2): ReLU(inplace=True)\n",
+       "      (3): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False)\n",
+       "      (4): Conv2d(4, 4, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))\n",
+       "      (5): BatchNorm2d(4, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
+       "      (6): ReLU(inplace=True)\n",
+       "      (7): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False)\n",
+       "    )\n",
+       "    (linear_layers): Sequential(\n",
+       "      (0): Linear(in_features=196, out_features=10, bias=True)\n",
+       "    )\n",
+       "  )\n",
+       ")"
       ]
      },
-     "execution_count": 57,
+     "execution_count": 90,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "test_logits = clf.predict_proba(X_test)\n",
-    "test_preds = softmax(test_logits, axis=1)\n",
-    "calibr.compute_ece(15, test_logits, y_test.to_numpy(), len(y_test))"
+    "calibr.temperature_scaling()"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/",
-     "height": 34
-    },
-    "colab_type": "code",
-    "id": "McvVpiIqR6Nj",
-    "outputId": "ed044e56-c766-457d-942a-7af91ac419f8"
-   },
+   "execution_count": 91,
+   "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "tensor(0.0211, dtype=torch.float64)"
+       "tensor([[-5.7242, -2.0955, -2.2245,  ...,  9.8173, -0.7770,  0.8910],\n",
+       "        [ 3.1985, -2.7507,  0.3069,  ..., -4.4638, -1.2120, -2.2296],\n",
+       "        [-2.6328, -4.6969,  7.7340,  ..., -3.8817, -2.4001, -3.3600],\n",
+       "        ...,\n",
+       "        [-0.9659, -0.9615, -2.7335,  ..., -0.5133,  1.3431, -1.5266],\n",
+       "        [-2.0694, -3.1440,  3.9460,  ...,  0.5145,  0.2711, -1.3649],\n",
+       "        [-0.1192, -1.5945,  0.3817,  ..., -4.0632, -0.5899, -1.9224]])"
       ]
      },
-     "execution_count": 11,
+     "execution_count": 91,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "calibr.ComputeTace(0.9, test_data, test_logits, 15, 'label')"
+    "val_logits_list = []\n",
+    "val_labels_list = []\n",
+    "for x_batch, y_batch in val_loader:\n",
+    "    val_logits_list.append(model(x_batch))\n",
+    "    val_labels_list.append(y_batch)\n",
+    "val_logits = torch.cat(val_logits_list)\n",
+    "val_labels = torch.cat(val_labels_list)\n",
+    "val_logits.detach_()"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 93,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "probs = f.softmax(val_logits, dim=-1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 94,
    "metadata": {},
    "outputs": [
     {
-     "data": {
-      "text/plain": [
-       "tensor([0.0025])"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ece  =  tensor([0.0296])\n",
+      "sce  =  tensor([0.0033])\n",
+      "ace  =  tensor(0.0310)\n",
+      "tace  =  tensor(0.0147)\n"
+     ]
     }
    ],
    "source": [
-    "calibr.compute_sce(15, 'label', test_logits, test_data)"
+    "compute_errors(n_bins=15, probs=probs.numpy(), labels=val_labels.numpy(),\n",
+    "               len_dataset=np.shape(probs)[0], threshold=0.9)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 95,
    "metadata": {},
    "outputs": [
     {
-     "data": {
-      "text/plain": [
-       "tensor(0.0251, dtype=torch.float64)"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Parameter containing:\n",
+      "tensor([0.6217], requires_grad=True)\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(calibr.temperature)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 96,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "temp_scaling_logits = torch.true_divide(val_logits, calibr.temperature)\n",
+    "temp_scaling_probs = f.softmax(temp_scaling_logits, dim=1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 97,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ece  =  tensor([0.0085])\n",
+      "sce  =  tensor([0.0015])\n",
+      "ace  =  tensor(0.0182)\n",
+      "tace  =  tensor(0.0070)\n"
+     ]
     }
    ],
    "source": [
-    "calibr.ComputeAce(15, test_data, 'label', test_logits)"
+    "compute_errors(n_bins=15, probs=temp_scaling_probs.detach().numpy(), labels=val_labels.numpy(),\n",
+    "               len_dataset=np.shape(probs)[0], threshold=0.9)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 40,
+   "execution_count": 98,
    "metadata": {
     "colab": {
      "base_uri": "https://localhost:8080/",
      "height": 34
     },
     "colab_type": "code",
-    "id": "rUPNsBe5WHet",
-    "outputId": "52673060-ebb3-4b6f-8dc9-f3d38ed980ef"
+    "id": "McvVpiIqR6Nj",
+    "outputId": "ed044e56-c766-457d-942a-7af91ac419f8"
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "tensor([0.0148])"
+       "torch.int64"
       ]
      },
-     "execution_count": 40,
+     "execution_count": 98,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "calibr.TemperatureScaling()\n",
-    "new_logits = calibr.scale_logits_with_temperature(test_logits).detach().numpy()\n",
-    "calibr.compute_ece(15, new_logits, y_test.to_numpy(), len(y_test))"
+    "calibr = calibrator.ModelWithVectScaling(model, logits, labels).float()\n",
+    "labels.dtype"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 58,
+   "execution_count": 99,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "tensor(0.0092, dtype=torch.float64)"
+       "ModelWithVectScaling(\n",
+       "  (model): Net(\n",
+       "    (cnn_layers): Sequential(\n",
+       "      (0): Conv2d(1, 4, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))\n",
+       "      (1): BatchNorm2d(4, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
+       "      (2): ReLU(inplace=True)\n",
+       "      (3): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False)\n",
+       "      (4): Conv2d(4, 4, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))\n",
+       "      (5): BatchNorm2d(4, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
+       "      (6): ReLU(inplace=True)\n",
+       "      (7): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False)\n",
+       "    )\n",
+       "    (linear_layers): Sequential(\n",
+       "      (0): Linear(in_features=196, out_features=10, bias=True)\n",
+       "    )\n",
+       "  )\n",
+       ")"
       ]
      },
-     "execution_count": 58,
+     "execution_count": 99,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "calibr.ComputeTace(0.9, test_data, new_logits, 15, 'label')\n"
+    "calibr.vector_scaling(lr=0.01, max_iter=50)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 100,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "vect_scaling_logits = calibr.vector_scaling_logits(val_logits)\n",
+    "vect_scaling_probs = f.softmax(vect_scaling_logits, dim=1)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 59,
+   "execution_count": 101,
    "metadata": {},
    "outputs": [
     {
-     "data": {
-      "text/plain": [
-       "tensor(0.0231, dtype=torch.float64)"
-      ]
-     },
-     "execution_count": 59,
-     "metadata": {},
-     "output_type": "execute_result"
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ece  =  tensor([0.0183])\n",
+      "sce  =  tensor([0.0024])\n",
+      "ace  =  tensor(0.0224)\n",
+      "tace  =  tensor(0.0110)\n"
+     ]
     }
    ],
    "source": [
-    "calibr.ComputeAce(15, test_data, 'label', new_logits)"
+    "compute_errors(n_bins=15, probs=vect_scaling_probs.detach().numpy(), labels=val_labels.numpy(),\n",
+    "               len_dataset=np.shape(probs)[0], threshold=0.9)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 60,
+   "execution_count": 102,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "tensor([0.0021])"
+       "Parameter containing:\n",
+       "tensor([ 1.0942e+00,  1.0579e+00,  1.0807e+00,  1.0858e+00,  1.1143e+00,\n",
+       "         1.0998e+00,  1.0911e+00,  1.1073e+00,  1.0508e+00,  1.1783e+00,\n",
+       "        -9.8967e-04,  1.2546e-03, -7.5154e-03,  7.0824e-03,  2.1402e-03,\n",
+       "        -1.2270e-02, -2.2263e-03,  9.1528e-03, -1.4546e-02,  1.7918e-02],\n",
+       "       requires_grad=True)"
       ]
      },
-     "execution_count": 60,
+     "execution_count": 102,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "calibr.compute_sce(15, 'label', new_logits, test_data)"
+    "calibr.W_and_b"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 37,
+   "execution_count": 103,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "0.01349574089747102"
+       "ModelWithMatrScaling(\n",
+       "  (model): Net(\n",
+       "    (cnn_layers): Sequential(\n",
+       "      (0): Conv2d(1, 4, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))\n",
+       "      (1): BatchNorm2d(4, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
+       "      (2): ReLU(inplace=True)\n",
+       "      (3): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False)\n",
+       "      (4): Conv2d(4, 4, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))\n",
+       "      (5): BatchNorm2d(4, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
+       "      (6): ReLU(inplace=True)\n",
+       "      (7): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False)\n",
+       "    )\n",
+       "    (linear_layers): Sequential(\n",
+       "      (0): Linear(in_features=196, out_features=10, bias=True)\n",
+       "    )\n",
+       "  )\n",
+       ")"
       ]
      },
-     "execution_count": 37,
+     "execution_count": 103,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "new_probs = calibrator.multiclass_histogram_binning(15, logits, y_cal.to_numpy(), test_logits)\n",
-    "\n",
-    "def SplitIntoBins(m, preds, labels):\n",
-    "    bins = []\n",
-    "    true_labels_for_bins = []\n",
-    "    for i in range(m):\n",
-    "            bins.append([])\n",
-    "            true_labels_for_bins.append([])\n",
-    "    for j in range(len(labels)):\n",
-    "            max_p = max(preds[j])\n",
-    "            for i in range(m):\n",
-    "                if i/m < max_p and max_p <= (i+1)/m:\n",
-    "                    bins[i].append((preds[j]))\n",
-    "                    true_labels_for_bins[i].append(labels[j])\n",
-    "    return bins, true_labels_for_bins\n",
-    "\n",
-    "def ComputeEce(m, preds, labels):\n",
-    "    bins, true_labels_for_bins = SplitIntoBins(m, preds, labels)\n",
-    "    accuracies = []\n",
-    "    confidences = []\n",
-    "    ece = 0\n",
-    "    bins = list(filter(None, bins))\n",
-    "    true_labels_for_bins = list(filter(None, true_labels_for_bins))\n",
-    "    for i in range(len(bins)):\n",
-    "        accuracy = accuracy_score(true_labels_for_bins[i], np.argmax(bins[i], axis=1))\n",
-    "        accuracies.append(accuracy)\n",
-    "        max_pi = sum(np.amax(bins[i], axis = 1))\n",
-    "        confidences.append(max_pi/len(bins[i]))\n",
-    "        ece += len(bins[i]) * abs(accuracies[i] - confidences[i])/2897\n",
-    "    return ece\n",
-    "ComputeEce(15, new_probs, y_test.to_numpy())"
+    "calibr = calibrator.ModelWithMatrScaling(model, logits, labels).float()\n",
+    "calibr.matrix_scaling(lr=0.0001, max_iter=1000)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 41,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/",
-     "height": 85
-    },
-    "colab_type": "code",
-    "id": "uUSoNf8XoWHp",
-    "outputId": "0a716825-bf17-4344-92c6-54dec28aba40"
-   },
+   "execution_count": 104,
+   "metadata": {},
    "outputs": [],
    "source": [
-    "y_true = []\n",
-    "for i in range(10):\n",
-    "    y_true.append([])\n",
-    "for i in range(10):\n",
-    "    for label in y_test:\n",
-    "        if label == i:\n",
-    "            y_true[i].append(1)\n",
-    "        else:\n",
-    "            y_true[i].append(0)                    "
+    "matr_scaling_logits = calibr.matrix_scaling_logits(val_logits)\n",
+    "matr_scaling_probs = f.softmax(matr_scaling_logits, dim=1)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 45,
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/",
-     "height": 34
-    },
-    "colab_type": "code",
-    "id": "gpigDxzW1NzT",
-    "outputId": "ee75b408-7706-4a8d-b897-9d2b5e951606"
-   },
+   "execution_count": 105,
+   "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"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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nCnSRALP3SDYjE9cyK2kHzWqF896tCWfWTKugHb84jbUOpUKPF+Gie9VYqxRToIsEkDyXZcBbP5B2MItHujfh7isaUj74LDp8WAs/T4A5j0JYJNw2B+I6eL5g8SgFukgA2JWeRVRlp5nWP65uSd3qlWhc8yz7jR/LhNl/h18+hgad4br3nFCXUk/NuUT8mMtlmbh0K11f+56Plm0FoHOz6LMP870b4L2u8Msn0OkJ5+KnwtxvaIQu4qc27TnC8Gmr+XHzfi5tFEmnptHn9oZrp8PMvzi37d88FRp19UyhUmIU6CJ+6LPl23hm5loqlAvi5QFtuP6Cumd+t+dxWxY70xFTf4S67Z3GWlXrerReKRkKdBE/VLd6KJ2aOs20oqu42Uwr5yikp8HhHc5/09Oc5eGSZwIWgso5jbUU5n5LgS7iB7Jz8/jvtxsAeKRHoWZa1jp3bqanOet2Hk77M7D/CPDtzkLNhQVXAOyf75OyFOIvKZmDEo9ToIuUZq48ktb/xtufLyLv4HZ61XNhvzaYgqPs9DTIPXrya8OioUptqBYHsR2cz6vEQHj+f6vUht2/wvi+kHcMgkMg/rKSP0bxGGOt9cmOExIS7IoVK3yyb5FSIScrfzSdH86FRtau9DQ4vIsg8k58XVB5J4zD6xQK6Tp/flSuBeVC3Ksj5UfYstAJ89j2nj9O8ShjzE/W2oSinnNrhG6M6Qn8GwgG3rPWvlTENgOBkTh/v/1irb3xrCsW8WfWQtahQiGdf9qj4Mj66P6TXxsSnh/SdThS5xI+/DWXuLiGdL2oLZUi6jrhHVoDgjw44zi2vYI8QBQb6MaYYOBN4EogFVhujEm01iYX2KYx8ARwibX2gDHmHOdPifjYqUatrjzI2OOEc1Ej6+OBnZN58nuGRTkj6aqxzntWqZM/ys7/CK/NIVclZq/ewY0d4qgCXJeeRU13L3pKmefOCL09sMFauwnAGPMp0A9ILrDNXcCb1toDANba3Z4uVKTEpPwI46921skMCoa4iyE3K/+C4w6whU+BlPvz9Eet1tC4xx+j7D8CO7wWlKtw2t1+uWYnT8/8kf0Zx+jQIIKGUZUV5nJG3An0GCClwONUoHBThyYAxpjFOKdlRlprvyz8RsaYYcAwgLi4uLOpV8T7Vk92AhzAletcOKzZEupf9sdI+o+LilViIDTynE6B7D6cxcjEtcxZvZMWtavw/m0X0jDqLJtpSZnmTqAXdbdC4Sup5YDGQCegLrDQGNPKWnvwhBdZOwYYA85F0TOuVsTbVn4IP33gfG6CnGl9gz/x2jnmPJdl4NtLSDuUxaM9mjLs8gZn10xLBPcCPRWILfC4LpBWxDZLrbU5wGZjzHqcgF/ukSpFvC0nC754DH4eD/Uvd1av37XGazM/dhw6Ss3wik4zrb4tia0eevYtbkXyuRPoy4HGxpj6wHZgEFB4BssMYDDwgTEmEucUzCZPFiriNQe3wWdDYMcquPQh6PwUBJeDJj08viuXyzJhyRZenrue4b2accvF8XQ+1x4sIvmKDXRrba4x5gFgLs758XHW2rXGmOeAFdbaxPznuhtjkoE84FFr7T5vFi7iERu+gal3OrNXBn0Mzfp4b1e7jzB8ahIrth7g8iZRdGmmIBfP0o1FUja5XLDwVZj3AkS3gBsmQo2GXtvdpz9u45nEtVQqH8wzV7Wgf7uYs2+mJWXaOd9YJBJQMvfD9Lvh96+gzQ1w1WgICfPqLuNqhNKteTTP9m1FVPjppy+KnC0FupQtO36Bz2525pT3fhUuvNMra2Rm5eTxn29/B+Cxns3o2DCSjg21UIR4lwJdyo6VH8Ksh50VeG7/AmIv9MpuVmzZz2NTk9i0J4NBF8ZirdXpFSkRCnQJfIWnJA543yvLqh3JzuWVL9cxYelWYqpVYsId7bm8SZTH9yNyKgp0CWynmpLoBTsPHeXT5SncenE8j/ZoSlgF/XpJydJPnASuEpiSeCDjGLNW72DIRfVoFB3Owsc6u7+CkIiHKdAl8LhcsOAVmP+i16YkWmv5Ys1Onpm5hoOZOXRsWIOGUZUV5uJTCnQJLCUwJXF3ehZPz1zD3LW7aB1TlQl3dFAzLSkVFOgSOEpgSmKey3L9O0vYeSiLJ3o1Y+il9SmnZlpSSijQJTB4eUpi2sGj1KriNNN6rl8rYqtXooFG5VLKaGgh/i0nCxIfhJn3Q1wHuHuBR8M8z2V5f/Fmur72PR8u2wrAFU2iFOZSKmmELv7rwFaYdEv+lMSHoctTzgpDHrJh92Eem5LEz9sO0qlpFF2b1/TYe4t4gwJd/NPv38A0701J/HjZNkYmriWsQjCjbziPa85XMy0p/RTo4l9KYEoiQHxkKN1b1mRk35ZEVlYzLfEPCnTxHydNSXwDQkI98tZZOXmM/uY3DIbhvdRMS/yTAl38Q9oqmDTEK1MSl23ax/Bpq9m8N4ObOsSpmZb4LQW6lH4/T4TZf/f4lMTDWTn868t1fLh0G3ERoXx8Zwc6NtKoXPyXAl1Kr5ws+OJR+HkC1L8CBozzaJfEXenZTPkplTsvrc/D3ZsQGqJfB/Fv+gmW0slLUxL3ZxxjdlIaQy6Op1F0ZRY+1kUrCEnAUKBL6eOFKYnWWmYl7WBk4lrSs3K4pFEkDaIqK8wloCjQpfTw0pTEXelZjJi+hm9+3UWbulX5aEAH3ekpAUmBLqVD5n6YNgw2fA1tBuV3STz3KYl5LsvA/GZaI3o35/ZL4tVMSwKWAl18r+CUxD6vQcLQc56SmHogk9pVKxEcZBjVrxVxEaHER3q2ja5IaaOhivjWzxNhbHfnfPkdX57z/PI8l+W9hZvo9vr3fLjUaaZ1eZMohbmUCRqhi294YUri+p2HeWxqEr+kHKRrs2i6t1QzLSlbFOhS8rwwJfHDpVt59vO1hFcsz78HnU/f8+robk8pcxToUrL+mJLo8siUxOO36TeKrkzv1rV55qoW1FAzLSmjFOhSMlwuWPAyzH8JaraEgRPOaUri0WN5vP71eoKCDE/0as5FDWpwUYMaHixYxP8o0MX7PDwlccnGfQyflsTWfZkMuaiemmmJ5FOgi3d5cEpielYOL85Zxyc/bqNejVA+vquDWtyKFKBAF+/5eQLMfsSZvXLHl1A34Zzebnd6NjNWbmfY5Q14qFsTKoV4brk5kUDg1jx0Y0xPY8x6Y8wGY8zw02w3wBhjjTHn9psr/i0nC2Y+AIl/gXoXOws3n2WY7zuSzQeLNwPQKLoyix7vzJO9myvMRYpQ7AjdGBMMvAlcCaQCy40xidba5ELbhQMPAsu8Uaj4iQNbnVMsO36By/4OnUec1ZREay2Jv6QxMnEtR7JzubxJFA2iKmsGi8hpuHPKpT2wwVq7CcAY8ynQD0gutN0o4GXgEY9WKP7jhCmJn0Cz3mf1NmkHj/LUjDV8t24358dW4+UBbdRMS8QN7gR6DJBS4HEq0KHgBsaYtkCstXaWMeaUgW6MGQYMA4iLizvzaqV08uCUxNw8F4PGLGXP4WyevqoFt3WMJzhIM1hE3OFOoBf122T/eNKYIGA0cFtxb2StHQOMAUhISLDFbC7+wENTElP2Z1KnWiXKBQfxwrWtiYsIJa6GZxaAFikr3LkomgrEFnhcF0gr8DgcaAXMN8ZsAS4CEnVhtAxIWwVjroBN86HP63Dt22cc5rl5LsYs2Ei3179n4pItAFzaOFJhLnIW3BmhLwcaG2PqA9uBQcCNx5+01h4C/pgMbIyZDzxirV3h2VKlVPHAlMRfd6Tz+NQkklIPcWWLmvRqXdsLhYqUHcUGurU21xjzADAXCAbGWWvXGmOeA1ZYaxO9XaSUIjlZMOcRWDkRGnSC68aeVZfEiUu28OznyVStVJ7/3diWPq1r625PkXPk1o1F1to5wJxCX3vmFNt2OveypFTywJTE47fpN6kZztXn1eHpq1oQERbipYJFyhbdKSru+f1rmHonWHtWUxIzj+Xy6tzfKBdseLJ3czo0qEEHNdMS8SitWCSn53LBvBfho+uhal0YNu+Mw3zxhr30eGMB4xZv5liuC2s1wUnEGzRCl6Kl/Ai/fwUb58H2FXDeYGcmyxnMYjl0NIcXZv/KZytSqB8ZxqS7L6Z9/QgvFi1StinQ5WQpP8IHV0FetvO444Nw5XNn3CVx75FsPk9K454rGvK3bo2pWF79V0S8SYEuJ7IWFo3+M8xNEFSq5naY7zmczee/pHHHpfVpGFWZRY930UVPkRKiQJc/ZR+BWQ/B+jlOkGMgOATiLyv2pdZaZqzazrOfJ5OZnUfnZtHUjwxTmIuUIAW6OPash8+GwN7foPNTTohvW+z8N7b9aV+6/eBRRkxfzfz1e2gX5zTTqh8ZVkKFi8hxCnSB1VMg8UEoXwmGTIeGnZ2v17uo2Jc6zbSWsO/IMUZe3YIhF6uZloivKNDLstxsmPskLH8P4i6GAeOgSh23XrptXyYx1Z1mWi/1b0NcRCixEeq/IuJLmodeVh3YCuN6OGHe8S9w6+duhXlunou35m+k2+jvmbBkCwCXNIpUmIuUAhqhl0Xrv4TpdzszWm74CJpf5dbL1qYd4vGpSazZnk6PljXpo2ZaIqWKAr0sycuFec/DotehVmtnIYqIBm69dPwPWxg1K5lqoSG8dVM7dUYUKYUU6GXF4V0w5Q7Yugja3Qq9/uVcBC3G8WZazWqF0+/8GJ6+qjnVQjUVUaQ0UqCXBVsWOWGelQ7XvA3nDy72JRnZubwydz3lgw0j+rRQMy0RP6CLooHM5YKFr8P4q6FCONz1rVthvuC3PXQfvYDxS7aQk2fVTEvET2iEHqgy98OMe+G3L6HltdD3v06on8ahzBxGzU5myk+pNIhymmldGK9mWiL+QoEeiLb/DJNuhcM7oNcr0P4ut3qx7M3I5ovVO7ivU0Me7KpmWiL+RoEeSKyFFWPhyyegck231vrcfTiLxFVp3HlZgz+aaVVX/xURv6RADxTZR+Dzv8KaKdDoSug/BkJPfbrEWsvUn7czalYyR3Py6Nq8JvUjwxTmIn5MgR4Idq+DSbfAvt+hy1Nw6d8h6NTXu1P2Z/Lk9NUs/H0vCfWq89J1aqYlEggU6P4uaZIzMg8JgyEzoMEVp908N8/F4HeXciDjGKP6teSmDvUIUjMtkYCgQPdXOVkw9wlYMQ7iOuY31jr13Ztb9mYQGxFKueAgXh7gNNOqW139V0QCieah+6MDW2BcdyfML/lrfmOtosM8J8/Fm/M20H30gj+aaXVsGKkwFwlAGqH7m3VzYMY9YIFBn0Cz3qfcdM32Qzw2JYnkHen0aV2bq9q41xpXRPyTAt1f5OXCd6Ng8RtQ+zy4fjxE1D/l5u8v3sw/Z/9KRFgIb998AT1b1SrBYkXEFxTo/uDwzvzGWovhgtuh50tQvmKRmx5vptWyTlX6t43hqT4tqBpavoQLFhFfUKCXdpsXwJShcOwIXPsOnDeoyM2OZOfy8pfrCAkO4qmrWtC+fgTt6+u2fZGyRBdFSyuXCxa+BhP6QcWqcNd3pwzz+et302P0AiYu3YoFNdMSKaM0Qi+NMvc7Kwr9/hW0ug6u/neRjbUOZBxj1Oxkpv28nUbRlZlyT0cuqFfdBwWLSGmgQC9ttv8Ek25zGmv1fhUuvPOUjbUOZB7jq7W7eLBLI+7v0ogK5dRMS6Qsc+uUizGmpzFmvTFmgzFmeBHPP2yMSTbGJBljvjXG1PN8qQHOWvjxXRjbA7Bwx9wiuyTuTs9izIKNWGtpEFWZxY934eHuTRXmIlL8CN0YEwy8CVwJpALLjTGJ1trkAputBBKstZnGmHuBl4EbvFFwQMo+nN9Yayo07u5c/CzUWMtay+QVqYyancyxXBdXtqhF/cgwzWARkT+4c8qlPbDBWrsJwBjzKdAP+CPQrbXzCmy/FLjZk0UGtN2/wmdDYP9G6PoMXPLQSY21UvZn8sS01SzasJf29SN4qX9rNdMSkZO4E+gxQEqBx6lAh9NsPxT4oqgnjDHDgGEAcXFxbpYYwH75FGY9BCGV4ZaZUP/ykzY53kzrYGYO/7ymFTe2j1MzLREpkjuBXlR6FDkvzhhzM5AAFNnyz1o7BhgDkJCQUHbn1uVkwZePw08fQL1LnMZa4cePmo4AAAsvSURBVCfeybl5bwZx+c20XhlwHvVqhFKnWiXf1CsifsGdi6KpQGyBx3WBtMIbGWO6ASOAvtbabM+UF4D2b4axVzphfsnf4JbEE8I8J8/Ff7/9nR6jFzD+hy0AXNywhsJcRIrlzgh9OdDYGFMf2A4MAm4suIExpi3wDtDTWrvb41UGinWzYfq9zt88gz+Fpr1OeDop9SCPTUli3c7DXH1eHfqer2ZaIuK+YgPdWptrjHkAmAsEA+OstWuNMc8BK6y1icArQGVgsnGm2W2z1vb1Yt3+JS8Hvn0OfvgP1D4fBo6H6vEnbDJu0Wb+OTuZqPAKvHtLAle2qOmbWkXEb7l1Y5G1dg4wp9DXninweTcP1xU40nfAlNth2xJIGAo9XjihsdbxZlpt6lblhgtjGd6rOVUraSqiiJw53SnqTZvmw9Q74VgG9H8P2lz/x1OHs3J46Yt1VCgXzDNXtyAhPoKEeDXTEpGzp+Zc3uBywfevwMRroVJ1uGveCWE+b91uuo9ewCc/bqNcsFEzLRHxCI3QPS1zP0wbBhu+hlYD8htrVQZgf8Yxnvt8LTNWpdGkZmX+76aOtI1TMy0R8QwFuielroDJt8GRXdDnNeeceYFeLIeO5vDtr7v5a9fG3N+5ESHl9AeSiHiOAt0TjjfWmvskhNd2GmvFtANg56EsZqzazt2XN6B+ZBiLhnfRRU8R8QoF+rnKPgyJf4G106FJT7jmLQiNwFrLp8tTeGH2r+S4XPRsWYv4yDCFuYh4jQL9XOxKhkm35DfW+odz52dQEFv3ZTB86mqWbNrHRQ0ieKl/G+LVTEtEvEyBfrZWfeI01qoQ7ty+X/8ywGmmdeO7yzh0NIcXrm3NoAtj1UxLREqEAv1M5WTBF4/Bz+Oh3qUwYCyE12LjniPUy2+m9dpAp5lW7arqvyIiJUfTLM7E/k0wtpsT5pc+DLfM5FilaN745jd6vrGACUu2AnBRgxoKcxEpcRqhu+vXWTDjPmca4uDPoGlPVqUc5PEpSazfdZh+59fhmrYxvq5SRMowBXpx8nLgm5Gw5H9Qpy1cPx6q12Psos08PzuZ6PCKjL01ga7N1UxLRHxLgX466Wkw+XZIWQoX3gk9XsAGh2CA82OrMqh9HMN7NaNKRU1FFBHfU6CfysZ5TmOtnKNw3VjSG/fjxcR1VCwfxD+ubskF9SK4oJ6aaYlI6aGLooW5XPD9y05jrbBIGDaPb4Iv48rXv+ez5dsIKRekZloiUipphF5Qxj6Ydhds/BZaD2Rf53/x7NytJP6ygWa1whkzJIHzYqv5ukoRkSIp0I9LWQ6Tb4WMPXDVaLjgdg7vy2Te+t081K0J93ZqqGZaIlKqKdCthWVvw1dPQZU67Bn4OZPSIrkPiI8MY/HwLrroKSJ+oWwHelY6JD4AyTOxTXoyOfYpnvs4jTzXQfq0rk18ZJjCXET8RtkN9F1r4bMhcGAL+zuO4L5Nl7B09jYuaVSDF69tQ1yNUF9XKCJyRspmoK/6GGY9DBWrkDtkJldPyiE96wgvX9eG6xPqYoyaaYmI/ylbgZ5zFOY8CisnkhnTkZCB4yhXtTajb9hPvRqh1KxS0dcVioictbIzbWPfRnjvSlg5kWV1b6ft5vsYvzoLgPb1IxTmIuL3ysYIPTkRZt5PrjX8o9LTfLShOf3bxtBfzbREJIAEdqAXaKy1O7wl/fcOw1Ullvdvb03nptG+rk5ExKMCN9APbYcpt0PKMmg/jNRmD9MpaS+P92xGuKYiikgACsxA3/gdril3kpOdycz4ZxnY+2+0A9o1qO3rykREvCawLoq68mD+S9iJ/dl8NJSrskaxpVZPNdMSkTIhcEboGXs5NnkoIVvmMy3vUj6s8TdGX9+eVjFVfV2ZiEiJCIxA37YMJt9G+cx9PMswIjsPY9IVDSkfHFh/gIiInI5/B7q1HJz3H8IXPktQ1bqYoV/x9xqtqFzBvw9LRORsuDWENcb0NMasN8ZsMMYML+L5CsaYz/KfX2aMifd0oYW5Mg+y9e0BVFvwDPNcbUm5/kuoc77CXETKrGID3RgTDLwJ9AJaAIONMS0KbTYUOGCtbQSMBv7l6UIL2rXwfY680oqYnd/ySdU7afpgInExdby5SxGRUs+dEXp7YIO1dpO19hjwKdCv0Db9gPH5n08BuhovdbjKXfkJ0d/+jXB7GBNcnkHXDSS2Rpg3diUi4lfcCfQYIKXA49T8rxW5jbU2FzgE1Cj8RsaYYcaYFcaYFXv27DmrgssdTgMMBgi2eZiti87qfUREAo07gV7USLvwxG53tsFaO8Zam2CtTYiKinKnvpPVvwxTriKYYAgOgfjLzu59REQCjDtXEFOB2AKP6wJpp9gm1RhTDqgK7PdIhYXFtodbE2HLQifMY9t7ZTciIv7GnUBfDjQ2xtQHtgODgBsLbZMI3AosAQYA31lv3p4Z215BLiJSSLGBbq3NNcY8AMwFgoFx1tq1xpjngBXW2kRgLDDRGLMBZ2Q+yJtFi4jIydyatG2tnQPMKfS1Zwp8ngVc79nSRETkTOjeeBGRAKFAFxEJEAp0EZEAoUAXEQkQxleLPxhj9gBbz/LlkcBeD5bjD3TMZYOOuWw4l2OuZ60t8s5MnwX6uTDGrLDWJvi6jpKkYy4bdMxlg7eOWadcREQChAJdRCRA+Gugj/F1AT6gYy4bdMxlg1eO2S/PoYuIyMn8dYQuIiKFKNBFRAJEqQ700rg4tbe5ccwPG2OSjTFJxphvjTH1fFGnJxV3zAW2G2CMscYYv5/i5s4xG2MG5n+v1xpjPi7pGj3NjZ/tOGPMPGPMyvyf796+qNNTjDHjjDG7jTFrTvG8Mcb8J//fI8kY0+6cd2qtLZUfOK16NwINgBDgF6BFoW3uA97O/3wQ8Jmv6y6BY+4MhOZ/fm9ZOOb87cKBBcBSIMHXdZfA97kxsBKonv842td1l8AxjwHuzf+8BbDF13Wf4zFfDrQD1pzi+d7AFzgrvl0ELDvXfZbmEXqpWpy6hBR7zNbaedbazPyHS3FWkPJn7nyfAUYBLwNZJVmcl7hzzHcBb1prDwBYa3eXcI2e5s4xW6BK/udVOXllNL9irV3A6Vdu6wdMsI6lQDVjTO1z2WdpDnSPLU7tR9w55oKG4vwf3p8Ve8zGmLZArLV2VkkW5kXufJ+bAE2MMYuNMUuNMT1LrDrvcOeYRwI3G2NScdZf+EvJlOYzZ/r7Xiy3FrjwEY8tTu1H3D4eY8zNQAJwhVcr8r7THrMxJggYDdxWUgWVAHe+z+VwTrt0wvkrbKExppW19qCXa/MWd455MPCBtfY1Y8zFOKugtbLWurxfnk94PL9K8wj9TBanxuuLU5cMd44ZY0w3YATQ11qbXUK1eUtxxxwOtALmG2O24JxrTPTzC6Pu/mzPtNbmWGs3A+txAt5fuXPMQ4FJANbaJUBFnCZWgcqt3/czUZoD/Y/FqY0xITgXPRMLbXN8cWooicWpva/YY84//fAOTpj7+3lVKOaYrbWHrLWR1tp4a208znWDvtbaFb4p1yPc+dmegXMBHGNMJM4pmE0lWqVnuXPM24CuAMaY5jiBvqdEqyxZicAt+bNdLgIOWWt3nNM7+vpKcDFXiXsDv+FcHR+R/7XncH6hwfmGTwY2AD8CDXxdcwkc8zfALmBV/keir2v29jEX2nY+fj7Lxc3vswFeB5KB1cAgX9dcAsfcAliMMwNmFdDd1zWf4/F+AuwAcnBG40OBe4B7CnyP38z/91jtiZ9r3fovIhIgSvMpFxEROQMKdBGRAKFAFxEJEAp0EZEAoUAXEQkQCnQRkQChQBcRCRD/D5gJndC8sKIRAAAAAElFTkSuQmCC\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ece  =  tensor([0.0051])\n",
+      "sce  =  tensor([0.0014])\n",
+      "ace  =  tensor(0.0167)\n",
+      "tace  =  tensor(0.0061)\n"
+     ]
     }
    ],
    "source": [
-    "new_predictions = np.transpose(softmax(new_logits, axis=1))\n",
-    "for i in range(10):\n",
-    "    fop, mpv = calibration_curve(y_true[i], new_predictions[i])\n",
-    "    plt.plot([0, 1], [0, 1], linestyle='--')\n",
-    "    plt.plot(mpv, fop, marker='.')\n",
-    "    plt.show() "
+    "compute_errors(n_bins=15, probs=matr_scaling_probs.detach().numpy(), labels=val_labels.numpy(),\n",
+    "               len_dataset=np.shape(probs)[0], threshold=0.9)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
+   "execution_count": 106,
+   "metadata": {
+    "scrolled": true
+   },
    "outputs": [],
    "source": [
-    "calibr.MatrixScaling()\n",
-    "new_logits = calibr.matrix_scaling_logits(test_logits).detach().numpy()\n",
-    "calibr.compute_ece(15, new_logits, y_test.to_numpy(), len(y_test))"
+    "hist_binning_probs = calibrator.multiclass_histogram_binning(15, logits.numpy(), labels.numpy(), val_logits)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 108,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "ece  =  tensor([0.0069])\n",
+      "sce  =  tensor([0.0016])\n",
+      "ace  =  tensor(0.0177, dtype=torch.float64)\n",
+      "tace  =  tensor(0.0129, dtype=torch.float64)\n"
+     ]
+    }
+   ],
    "source": [
-    "calibr.VectorScaling()\n",
-    "new_logits = calibr.vector_scaling_logits(test_logits).detach().numpy()\n",
-    "calibr.compute_ece(15, new_logits, y_test.to_numpy(), len(y_test))"
+    "compute_errors(n_bins=15, probs=hist_binning_probs, labels=val_labels.numpy(),\n",
+    "               len_dataset=np.shape(probs)[0], threshold=0.9)"
    ]
   }
  ],
@@ -653,7 +695,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.2"
+   "version": "3.7.4"
   },
   "widgets": {
    "application/vnd.jupyter.widget-state+json": {

From 2602f28365481f428cd4dd0e34c73ca5960bc272 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=D0=9C=D0=B8=D1=85=D0=B0=D0=B8=D0=BB=20=D0=A2=D0=B5=D1=80?=
 =?UTF-8?q?=D0=B5=D1=88=D0=BA=D0=B8=D0=BD?= <tereshkin.ma@phystech.edu>
Date: Sun, 6 Sep 2020 19:39:19 +0300
Subject: [PATCH 4/8] Add function compute_erros, change names of methods

---
 examples/calibration_example.ipynb | 62 +++++++++++++++---------------
 1 file changed, 31 insertions(+), 31 deletions(-)

diff --git a/examples/calibration_example.ipynb b/examples/calibration_example.ipynb
index 27fd811..b83060b 100644
--- a/examples/calibration_example.ipynb
+++ b/examples/calibration_example.ipynb
@@ -6,7 +6,7 @@
    "metadata": {
     "colab": {
      "base_uri": "https://localhost:8080/",
-     "height": 34
+     "height": 34.0
     },
     "colab_type": "code",
     "id": "s0rU2DMvB2rL",
@@ -16,7 +16,7 @@
    "source": [
     "from sklearn.metrics import accuracy_score\n",
     "from scipy.special import softmax\n",
-    "import calibrator\n",
+    "import alpaca.calibrator as calibrator\n",
     "import numpy as np\n",
     "import pandas as pd\n",
     "from alpaca.dataloader.builder import build_dataset"
@@ -63,7 +63,7 @@
    "metadata": {
     "colab": {
      "base_uri": "https://localhost:8080/",
-     "height": 1000,
+     "height": 1000.0,
      "referenced_widgets": [
       "2605521ec37f472ebaeb2799fc46089a",
       "f4c70bba269d41cb96b367a43a631101",
@@ -205,7 +205,7 @@
    "metadata": {
     "colab": {
      "base_uri": "https://localhost:8080/",
-     "height": 153
+     "height": 153.0
     },
     "colab_type": "code",
     "id": "8qM2NebHB2ra",
@@ -336,7 +336,7 @@
     }
    ],
    "source": [
-    "calibr.temperature_scaling()"
+    "calibr.scaling()"
    ]
   },
   {
@@ -457,7 +457,7 @@
    "metadata": {
     "colab": {
      "base_uri": "https://localhost:8080/",
-     "height": 34
+     "height": 34.0
     },
     "colab_type": "code",
     "id": "McvVpiIqR6Nj",
@@ -513,7 +513,7 @@
     }
    ],
    "source": [
-    "calibr.vector_scaling(lr=0.01, max_iter=50)"
+    "calibr.scaling(lr=0.01, max_iter=50)"
    ]
   },
   {
@@ -522,7 +522,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "vect_scaling_logits = calibr.vector_scaling_logits(val_logits)\n",
+    "vect_scaling_logits = calibr.scaling_logits(val_logits)\n",
     "vect_scaling_probs = f.softmax(vect_scaling_logits, dim=1)"
    ]
   },
@@ -606,7 +606,7 @@
    ],
    "source": [
     "calibr = calibrator.ModelWithMatrScaling(model, logits, labels).float()\n",
-    "calibr.matrix_scaling(lr=0.0001, max_iter=1000)"
+    "calibr.scaling(lr=0.0001, max_iter=1000)"
    ]
   },
   {
@@ -615,7 +615,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "matr_scaling_logits = calibr.matrix_scaling_logits(val_logits)\n",
+    "matr_scaling_logits = calibr.scaling_logits(val_logits)\n",
     "matr_scaling_probs = f.softmax(matr_scaling_logits, dim=1)"
    ]
   },
@@ -1242,11 +1242,11 @@
       "description": " 93%",
       "description_tooltip": null,
       "layout": "IPY_MODEL_c5fbb54c30174247a4b890e22a96cd15",
-      "max": 50000,
-      "min": 0,
+      "max": 50000.0,
+      "min": 0.0,
       "orientation": "horizontal",
       "style": "IPY_MODEL_f95b3d10c84f400faa38c4396870d859",
-      "value": 46587
+      "value": 46587.0
      }
     },
     "3f677cdc4469460c852fe4d9a6979869": {
@@ -1438,11 +1438,11 @@
       "description": "Extraction completed...: 100%",
       "description_tooltip": null,
       "layout": "IPY_MODEL_b6689d61d6604d8981d446c538fbd44f",
-      "max": 1,
-      "min": 0,
+      "max": 1.0,
+      "min": 0.0,
       "orientation": "horizontal",
       "style": "IPY_MODEL_de3041298f1e496d93a8d58259cd7009",
-      "value": 1
+      "value": 1.0
      }
     },
     "547d771bf7d146a19ef02a463c28a496": {
@@ -1595,11 +1595,11 @@
       "description": "",
       "description_tooltip": null,
       "layout": "IPY_MODEL_05f0a259a8d643c1ae85ecde57be4981",
-      "max": 1,
-      "min": 0,
+      "max": 1.0,
+      "min": 0.0,
       "orientation": "horizontal",
       "style": "IPY_MODEL_fb2bc264a3ae41028b3d7bcabdfcc009",
-      "value": 1
+      "value": 1.0
      }
     },
     "8cf16a3e63e3413a9b873711757595d0": {
@@ -1632,11 +1632,11 @@
       "description": "Dl Completed...: 100%",
       "description_tooltip": null,
       "layout": "IPY_MODEL_94fe1defabd84e3a8d31f398aeaf1455",
-      "max": 1,
-      "min": 0,
+      "max": 1.0,
+      "min": 0.0,
       "orientation": "horizontal",
       "style": "IPY_MODEL_c2c2b28ffcae4bf29973bb229a663da3",
-      "value": 1
+      "value": 1.0
      }
     },
     "9263135419074499a42e519958ed514a": {
@@ -2043,11 +2043,11 @@
       "description": "Dl Size...: 100%",
       "description_tooltip": null,
       "layout": "IPY_MODEL_9263135419074499a42e519958ed514a",
-      "max": 1,
-      "min": 0,
+      "max": 1.0,
+      "min": 0.0,
       "orientation": "horizontal",
       "style": "IPY_MODEL_23306e469c1342b9921883cf33502298",
-      "value": 1
+      "value": 1.0
      }
     },
     "c2c2b28ffcae4bf29973bb229a663da3": {
@@ -2146,11 +2146,11 @@
       "description": "",
       "description_tooltip": null,
       "layout": "IPY_MODEL_a4bc6f0e24fb4242b5536d0906810dc1",
-      "max": 1,
-      "min": 0,
+      "max": 1.0,
+      "min": 0.0,
       "orientation": "horizontal",
       "style": "IPY_MODEL_59f6ddd1dfcb445a8fa9f2cc9a9eaf8b",
-      "value": 1
+      "value": 1.0
      }
     },
     "d416605b18cc46658e89c1d4cb42fe46": {
@@ -2169,11 +2169,11 @@
       "description": "  0%",
       "description_tooltip": null,
       "layout": "IPY_MODEL_f7f30d82a72146be891adeb94eeabfc3",
-      "max": 10000,
-      "min": 0,
+      "max": 10000.0,
+      "min": 0.0,
       "orientation": "horizontal",
       "style": "IPY_MODEL_29afad3a94774993a0f437e4ac2f9e2a",
-      "value": 0
+      "value": 0.0
      }
     },
     "d6ad79f1ff934926884a149184ea2731": {

From 21f82c45e074db1b37bf7d129fdd0599c8e39761 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=D0=9C=D0=B8=D1=85=D0=B0=D0=B8=D0=BB=20=D0=A2=D0=B5=D1=80?=
 =?UTF-8?q?=D0=B5=D1=88=D0=BA=D0=B8=D0=BD?= <tereshkin.ma@phystech.edu>
Date: Sun, 6 Sep 2020 19:40:51 +0300
Subject: [PATCH 5/8] change names of methods

---
 alpaca/calibrator.py | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/alpaca/calibrator.py b/alpaca/calibrator.py
index 2bf5328..58ef953 100644
--- a/alpaca/calibrator.py
+++ b/alpaca/calibrator.py
@@ -22,7 +22,7 @@ def _split_into_bins(n_bins, probs, labels):
             if i / n_bins < max_p and max_p <= (i + 1) / n_bins:
                 bins[i].append((probs[j]))
                 true_labels_for_bins[i].append(labels[j])
-    return np.array(bins, dtype=object), np.array(true_labels_for_bins, dtype=object)
+    return np.array(bins), np.array(true_labels_for_bins)
 
 
 def compute_ece(n_bins, probs, labels, len_dataset):
@@ -75,7 +75,7 @@ def _split_into_ranges(R, probs, labels):
         for i in range(j * math.floor(N / R), (j + 1) * math.floor(N / R)):
             bins[j].append(probs[i])
             true_labels[j].append(labels[i])
-    return np.array(bins, dtype=object), np.array(true_labels, dtype=object)
+    return np.array(bins), np.array(true_labels)
 
 
 def compute_ace(R, labels, probs):
@@ -169,7 +169,7 @@ def scaling(self, lr=0.00001, max_iter=3500):
         optimizer = optim.LBFGS([self.W_and_b], lr=lr, max_iter=max_iter)
 
         def eval():
-            loss = nll(self.vector_scaling_logits(self.logits), self.labels)
+            loss = nll(self.scaling_logits(self.logits), self.labels)
             loss.backward()
             return loss
 
@@ -199,7 +199,7 @@ def scaling(self, lr=0.001, max_iter=100):
         optimizer = optim.LBFGS([self.W, self.b], lr=lr, max_iter=max_iter)
 
         def eval():
-            loss = nll(self.matrix_scaling_logits(self.logits), self.labels)
+            loss = nll(self.scaling_logits(self.logits), self.labels)
             loss.backward()
             return loss
 

From 8a02b47c02db699bab79179b3f8700bd6dfcdd38 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=D0=9C=D0=B8=D1=85=D0=B0=D0=B8=D0=BB=20=D0=A2=D0=B5=D1=80?=
 =?UTF-8?q?=D0=B5=D1=88=D0=BA=D0=B8=D0=BD?= <tereshkin.ma@phystech.edu>
Date: Sat, 19 Sep 2020 18:55:39 +0300
Subject: [PATCH 6/8] Change "forward" in classes and arguments in "scaling"
 method, add docstring

---
 alpaca/calibrator.py | 90 ++++++++++++++++++++++++++++++--------------
 1 file changed, 61 insertions(+), 29 deletions(-)

diff --git a/alpaca/calibrator.py b/alpaca/calibrator.py
index 58ef953..1a42d9d 100644
--- a/alpaca/calibrator.py
+++ b/alpaca/calibrator.py
@@ -78,7 +78,7 @@ def _split_into_ranges(R, probs, labels):
     return np.array(bins), np.array(true_labels)
 
 
-def compute_ace(R, labels, probs):
+def compute_ace(R, probs, labels):
     dict_class_probs = _split_into_classes(labels, probs)
     summa = 0
     for item in dict_class_probs.keys():
@@ -95,7 +95,7 @@ def compute_ace(R, labels, probs):
     return ACE
 
 
-def _choose_data(threshold, labels, probs):
+def _choose_data(threshold, probs, labels):
     arr = torch.max(torch.from_numpy(np.array(probs)), dim=1)[0]
     arr.numpy()
     arr_with_indices = list(enumerate(arr))
@@ -112,32 +112,35 @@ def _choose_data(threshold, labels, probs):
     return chosen_labels, chosen_probs
 
 
-def compute_tace(threshold, labels, probs, R):
+def compute_tace(threshold, probs, labels, R):
     if isinstance(labels, pd.DataFrame) or isinstance(labels, pd.Series):
         labels = labels.to_numpy()
-    chosen_labels, chosen_probs = _choose_data(threshold, labels, probs)
-    return compute_ace(R, chosen_labels, chosen_probs)
-
+    chosen_labels, chosen_probs = _choose_data(threshold, probs, labels)
+    return compute_ace(R, chosen_probs, chosen_labels)
 
 class ModelWithTempScaling(nn.Module):
+    """
+    A wrapper for a model with temperature scaling
 
-    def __init__(self, model, logits, labels):
+    model: a classification neural network
+    n_classes: number of classes in the dataset
+    """
+    def __init__(self, model):
         super(ModelWithTempScaling, self).__init__()
         self.model = model
         self.temperature = nn.Parameter(torch.ones(1))
-        self.logits = logits
-        self.labels = labels
 
     def forward(self, input):
         logits = self.model(input)
-        return torch.true_divide(logits, self.temperature)
+        return f.softmax(torch.true_divide(logits, self.temperature), dim=1)
 
-    def scaling(self, lr=0.01, max_iter=50):
+    def scaling(self, logits, labels, lr=0.01, max_iter=50):
+        # logits and labels must be from calibration dataset
         nll = nn.CrossEntropyLoss()
         optimizer = optim.LBFGS([self.temperature], lr=lr, max_iter=max_iter)
 
         def eval():
-            loss = nll(torch.true_divide(self.logits, self.temperature), self.labels)
+            loss = nll(torch.true_divide(logits, self.temperature), labels)
             loss.backward()
             return loss
 
@@ -146,30 +149,38 @@ def eval():
 
 
 class ModelWithVectScaling(nn.Module):
-    def __init__(self, model, logits, labels):
+
+    """
+    A wrapper for a model with vector scaling
+
+    model:  a classification neural network
+    n_classes: number of classes in the dataset
+
+    """
+
+    def __init__(self, model, n_classes):
         super(ModelWithVectScaling, self).__init__()
         self.model = model
-        self.logits = logits.float()
-        self.labels = labels
         self.W_and_b = nn.Parameter(
-            torch.cat((torch.ones(logits.shape[1]), torch.zeros(logits.shape[1])), dim=0))
+            torch.cat((torch.ones(n_classes), torch.zeros(n_classes)), dim=0))
 
     def forward(self, input):
         logits = self.model(input)
-        return self.scaling_logits(logits)
+        return f.softmax(self.scaling_logits(logits), dim=1)
 
     def scaling_logits(self, logits):
+        # logits and labels must be from calibration dataset
         W = torch.diag(self.W_and_b[:logits.shape[1]])
         b = self.W_and_b[logits.shape[1]:]
         b = b.unsqueeze(0).expand(logits.shape[0], -1)
-        return torch.mm(logits, W) + b
+        return torch.mm(logits.float(), W) + b
 
-    def scaling(self, lr=0.00001, max_iter=3500):
+    def scaling(self, logits, labels, lr=0.00001, max_iter=3500):
         nll = nn.CrossEntropyLoss()
         optimizer = optim.LBFGS([self.W_and_b], lr=lr, max_iter=max_iter)
 
         def eval():
-            loss = nll(self.scaling_logits(self.logits), self.labels)
+            loss = nll(self.scaling_logits(logits), labels)
             loss.backward()
             return loss
 
@@ -178,28 +189,33 @@ def eval():
 
 
 class ModelWithMatrScaling(nn.Module):
-    def __init__(self, model, logits, labels):
+    """
+    A wrapper for a model with matrix scaling
+
+    model: a classification neural network
+    n_classes: number of classes in the dataset
+    """
+    def __init__(self, model, n_classes):
         super(ModelWithMatrScaling, self).__init__()
         self.model = model
-        self.logits = logits.float()
-        self.labels = labels
-        self.W = nn.Parameter(torch.diag(torch.ones(logits.shape[1])))
-        self.b = nn.Parameter(torch.zeros(logits.shape[1]))
+        self.W = nn.Parameter(torch.diag(torch.ones(n_classes)))
+        self.b = nn.Parameter(torch.zeros(n_classes))
 
     def forward(self, input):
         logits = self.model(input)
-        return self.scaling_logits(logits)
+        return f.softmax(self.scaling_logits(logits), dim=1)
 
     def scaling_logits(self, logits):
         self.b.unsqueeze(0).expand(logits.shape[0], -1)
-        return torch.mm(logits, self.W) + self.b
+        return torch.mm(logits.float(), self.W) + self.b
 
-    def scaling(self, lr=0.001, max_iter=100):
+    def scaling(self, logits, labels, lr=0.001, max_iter=100):
+        # logits and labels must be from calibration dataset
         nll = nn.CrossEntropyLoss()
         optimizer = optim.LBFGS([self.W, self.b], lr=lr, max_iter=max_iter)
 
         def eval():
-            loss = nll(self.scaling_logits(self.logits), self.labels)
+            loss = nll(self.scaling_logits(logits), labels)
             loss.backward()
             return loss
 
@@ -208,6 +224,14 @@ def eval():
 
 
 def binary_histogram_binning(num_bins, probs, labels, probs_to_calibrate):
+    """
+    histogram binning for  binary classification
+    :param num_bins: number of bins
+    :param probs: probabilities on calibration dataset
+    :param labels: labels of calibration dataset
+    :param probs_to_calibrate: initial probabilities on test dataset (which need to be calibrated)
+    :return: calibrated probabilities on test dataset
+    """
     bins = np.linspace(0, 1, num=num_bins)
     indexes_list = np.digitize(probs, bins) - 1
     theta = np.zeros(num_bins)
@@ -222,6 +246,14 @@ def binary_histogram_binning(num_bins, probs, labels, probs_to_calibrate):
 
 
 def multiclass_histogram_binning(num_bins, logits, labels, logits_to_calibrate):
+    """
+    histogram binning for multiclass classification
+    :param num_bins: number of bins
+    :param logits: logits on calibration dataset
+    :param labels: labels on calibration dataset
+    :param logits_to_calibrate: initial logits on test dataset (which need to be calibrated)
+    :return: calibrated probabilities on test dataset
+    """
     probs = softmax(logits, axis=1)
     probs_to_calibrate = softmax(logits_to_calibrate, axis=1)
     binning_res = []

From 95506080df9daa370c405b07f5b1c031723dac76 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=D0=9C=D0=B8=D1=85=D0=B0=D0=B8=D0=BB=20=D0=A2=D0=B5=D1=80?=
 =?UTF-8?q?=D0=B5=D1=88=D0=BA=D0=B8=D0=BD?= <tereshkin.ma@phystech.edu>
Date: Sat, 19 Sep 2020 18:57:26 +0300
Subject: [PATCH 7/8] Use forward instead of scaling_logits

---
 examples/calibration_example.ipynb | 285 +++++++++++++++--------------
 1 file changed, 144 insertions(+), 141 deletions(-)

diff --git a/examples/calibration_example.ipynb b/examples/calibration_example.ipynb
index b83060b..76c555f 100644
--- a/examples/calibration_example.ipynb
+++ b/examples/calibration_example.ipynb
@@ -2,11 +2,11 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 85,
+   "execution_count": 52,
    "metadata": {
     "colab": {
      "base_uri": "https://localhost:8080/",
-     "height": 34.0
+     "height": 34
     },
     "colab_type": "code",
     "id": "s0rU2DMvB2rL",
@@ -16,7 +16,7 @@
    "source": [
     "from sklearn.metrics import accuracy_score\n",
     "from scipy.special import softmax\n",
-    "import alpaca.calibrator as calibrator\n",
+    "import  alpaca.calibrator as calibrator\n",
     "import numpy as np\n",
     "import pandas as pd\n",
     "from alpaca.dataloader.builder import build_dataset"
@@ -24,7 +24,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 86,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -38,15 +38,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 87,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [],
    "source": [
     "def compute_errors(n_bins, probs, labels, len_dataset, threshold):\n",
     "    ece = calibrator.compute_ece(n_bins, probs, labels, len_dataset)\n",
     "    sce = calibrator.compute_sce(n_bins, probs, labels)\n",
-    "    ace = calibrator.compute_ace(n_bins, labels, probs)\n",
-    "    tace = calibrator.compute_tace(threshold, labels, probs, n_bins)\n",
+    "    ace = calibrator.compute_ace(n_bins, probs, labels)\n",
+    "    tace = calibrator.compute_tace(threshold, probs, labels, n_bins)\n",
     "    errors = {\n",
     "        'ece' : ece,\n",
     "        'sce' : sce,\n",
@@ -59,11 +59,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 74,
+   "execution_count": 4,
    "metadata": {
     "colab": {
      "base_uri": "https://localhost:8080/",
-     "height": 1000.0,
+     "height": 1000,
      "referenced_widgets": [
       "2605521ec37f472ebaeb2799fc46089a",
       "f4c70bba269d41cb96b367a43a631101",
@@ -134,7 +134,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 75,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
@@ -143,7 +143,7 @@
        "(10000, 784)"
       ]
      },
-     "execution_count": 75,
+     "execution_count": 5,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -169,7 +169,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 76,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -201,11 +201,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 77,
+   "execution_count": 7,
    "metadata": {
     "colab": {
      "base_uri": "https://localhost:8080/",
-     "height": 153.0
+     "height": 153
     },
     "colab_type": "code",
     "id": "8qM2NebHB2ra",
@@ -220,7 +220,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 78,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [
     {
@@ -228,21 +228,25 @@
      "output_type": "stream",
      "text": [
       "..............................................................................................\n",
-      "Train loss on last batch 0.5379677414894104\n",
+      "Train loss on last batch 0.6062002182006836\n",
       "..............................................................................................\n",
-      "Train loss on last batch 0.3088064193725586\n",
+      "Train loss on last batch 0.27029111981391907\n",
       "..............................................................................................\n",
-      "Train loss on last batch 0.22927790880203247\n",
+      "Train loss on last batch 0.17512232065200806\n",
       "..............................................................................................\n",
-      "Train loss on last batch 0.18548454344272614\n",
+      "Train loss on last batch 0.137984961271286\n",
       "..............................................................................................\n",
-      "Train loss on last batch 0.15679685771465302\n",
-      "Accuracy 0.962890625\n"
+      "Train loss on last batch 0.11777593940496445\n",
+      "..............................................................................................\n",
+      "Train loss on last batch 0.10504749417304993\n",
+      "..............................................................................................\n",
+      "Train loss on last batch 0.09596506506204605\n",
+      "Accuracy 0.974609375\n"
      ]
     }
    ],
    "source": [
-    "for epoch in range(5):\n",
+    "for epoch in range(7):\n",
     "    for x_batch, y_batch in train_loader: # Train for one epoch\n",
     "        print('.', end='')\n",
     "        prediction = model(x_batch)\n",
@@ -263,22 +267,22 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 88,
+   "execution_count": 9,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "tensor([[-6.1167, -8.9871,  3.8799,  ..., -7.2181,  7.8800, -6.4360],\n",
-       "        [-0.1971,  4.4322, -0.6775,  ..., -2.8865,  2.0842, -4.1036],\n",
-       "        [-3.9227, -3.9793, -0.0458,  ..., -0.7269, -1.2891, -0.3848],\n",
+       "tensor([[ 8.9512, -4.2500,  0.6798,  ..., -2.8549, -0.2391, -2.0600],\n",
+       "        [ 0.3614, -6.6645, -3.0572,  ..., -5.0718, -0.3500, -2.2592],\n",
+       "        [-1.1534, -2.4635, -4.5541,  ..., -3.0422,  4.0586,  0.1374],\n",
        "        ...,\n",
-       "        [-4.0691, -1.3082, -3.1546,  ..., -0.4103, -2.4649,  1.1635],\n",
-       "        [10.0700, -8.9821, -1.3832,  ..., -5.1656,  2.8142,  0.3769],\n",
-       "        [-7.6608, -3.4758, -6.1055,  ..., -0.1984,  0.0988,  6.5401]])"
+       "        [-1.9714,  6.2411, -1.3644,  ..., -0.1338, -0.8241, -1.2896],\n",
+       "        [-4.3371, -0.0501, -3.0126,  ..., -5.5163, -2.3426,  0.7490],\n",
+       "        [-1.5622, -3.2278,  1.4504,  ..., -2.4797, -1.2854, -0.3554]])"
       ]
      },
-     "execution_count": 88,
+     "execution_count": 9,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -296,16 +300,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 89,
+   "execution_count": 53,
    "metadata": {},
    "outputs": [],
    "source": [
-    "calibr = calibrator.ModelWithTempScaling(model, logits, labels)"
+    "calibr = calibrator.ModelWithTempScaling(model)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 90,
+   "execution_count": 54,
    "metadata": {},
    "outputs": [
     {
@@ -330,33 +334,39 @@
        ")"
       ]
      },
-     "execution_count": 90,
+     "execution_count": 54,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "calibr.scaling()"
+    "calibr.scaling(logits, labels)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 91,
+   "execution_count": 55,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "tensor([[-5.7242, -2.0955, -2.2245,  ...,  9.8173, -0.7770,  0.8910],\n",
-       "        [ 3.1985, -2.7507,  0.3069,  ..., -4.4638, -1.2120, -2.2296],\n",
-       "        [-2.6328, -4.6969,  7.7340,  ..., -3.8817, -2.4001, -3.3600],\n",
+       "tensor([[-5.9499e+00, -2.4130e+00,  3.5374e+00,  ..., -2.5871e+00,\n",
+       "         -1.1915e-02, -1.4973e+00],\n",
+       "        [-1.7524e+00,  6.0652e+00, -6.6139e-01,  ..., -1.5802e+00,\n",
+       "         -9.0216e-01, -1.8846e+00],\n",
+       "        [-3.2816e+00, -4.0238e+00, -4.9135e+00,  ...,  1.6583e+00,\n",
+       "         -1.2195e+00,  7.1447e+00],\n",
        "        ...,\n",
-       "        [-0.9659, -0.9615, -2.7335,  ..., -0.5133,  1.3431, -1.5266],\n",
-       "        [-2.0694, -3.1440,  3.9460,  ...,  0.5145,  0.2711, -1.3649],\n",
-       "        [-0.1192, -1.5945,  0.3817,  ..., -4.0632, -0.5899, -1.9224]])"
+       "        [-6.3742e+00, -5.2211e+00, -5.5002e+00,  ...,  2.3404e+00,\n",
+       "          6.5512e-01,  5.1969e+00],\n",
+       "        [-2.6708e+00,  7.7116e+00,  5.5328e-01,  ...,  1.7785e-01,\n",
+       "          1.3387e-01, -3.4737e+00],\n",
+       "        [-1.3014e+00,  7.1492e+00,  1.6999e-01,  ..., -1.9588e+00,\n",
+       "          1.4840e-03, -3.1460e+00]])"
       ]
      },
-     "execution_count": 91,
+     "execution_count": 55,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -374,26 +384,26 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 93,
+   "execution_count": 56,
    "metadata": {},
    "outputs": [],
    "source": [
-    "probs = f.softmax(val_logits, dim=-1)"
+    "probs = f.softmax(val_logits, dim=-1)\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 94,
+   "execution_count": 57,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "ece  =  tensor([0.0296])\n",
-      "sce  =  tensor([0.0033])\n",
-      "ace  =  tensor(0.0310)\n",
-      "tace  =  tensor(0.0147)\n"
+      "ece  =  tensor([0.0197])\n",
+      "sce  =  tensor([0.0024])\n",
+      "ace  =  tensor(0.0221)\n",
+      "tace  =  tensor(0.0119)\n"
      ]
     }
    ],
@@ -404,7 +414,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 95,
+   "execution_count": 58,
    "metadata": {},
    "outputs": [
     {
@@ -412,7 +422,7 @@
      "output_type": "stream",
      "text": [
       "Parameter containing:\n",
-      "tensor([0.6217], requires_grad=True)\n"
+      "tensor([0.6368], requires_grad=True)\n"
      ]
     }
    ],
@@ -422,67 +432,49 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 96,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "temp_scaling_logits = torch.true_divide(val_logits, calibr.temperature)\n",
-    "temp_scaling_probs = f.softmax(temp_scaling_logits, dim=1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 97,
+   "execution_count": 59,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "ece  =  tensor([0.0085])\n",
-      "sce  =  tensor([0.0015])\n",
-      "ace  =  tensor(0.0182)\n",
-      "tace  =  tensor(0.0070)\n"
+      "ece  =  tensor([0.0076])\n",
+      "sce  =  tensor([0.0014])\n",
+      "ace  =  tensor(0.0151)\n",
+      "tace  =  tensor(0.0056)\n"
      ]
     }
    ],
    "source": [
+    "temp_scaling_probs_list = []\n",
+    "for x_batch, y_batch in val_loader:\n",
+    "    temp_scaling_probs_list.append(calibr.forward(x_batch))\n",
+    "temp_scaling_probs = torch.cat(temp_scaling_probs_list)\n",
     "compute_errors(n_bins=15, probs=temp_scaling_probs.detach().numpy(), labels=val_labels.numpy(),\n",
     "               len_dataset=np.shape(probs)[0], threshold=0.9)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 98,
+   "execution_count": 60,
    "metadata": {
     "colab": {
      "base_uri": "https://localhost:8080/",
-     "height": 34.0
+     "height": 34
     },
     "colab_type": "code",
     "id": "McvVpiIqR6Nj",
     "outputId": "ed044e56-c766-457d-942a-7af91ac419f8"
    },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "torch.int64"
-      ]
-     },
-     "execution_count": 98,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
-    "calibr = calibrator.ModelWithVectScaling(model, logits, labels).float()\n",
-    "labels.dtype"
+    "calibr = calibrator.ModelWithVectScaling(model, n_classes=10).float()"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 99,
+   "execution_count": 61,
    "metadata": {},
    "outputs": [
     {
@@ -507,38 +499,40 @@
        ")"
       ]
      },
-     "execution_count": 99,
+     "execution_count": 61,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "calibr.scaling(lr=0.01, max_iter=50)"
+    "calibr.scaling(logits, labels, lr=0.001, max_iter=300)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 100,
+   "execution_count": 62,
    "metadata": {},
    "outputs": [],
    "source": [
-    "vect_scaling_logits = calibr.scaling_logits(val_logits)\n",
-    "vect_scaling_probs = f.softmax(vect_scaling_logits, dim=1)"
+    "vect_scaling_probs_list = []\n",
+    "for x_batch, y_batch in val_loader:\n",
+    "    vect_scaling_probs_list.append(calibr.forward(x_batch))\n",
+    "vect_scaling_probs = torch.cat(vect_scaling_probs_list)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 101,
+   "execution_count": 63,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "ece  =  tensor([0.0183])\n",
-      "sce  =  tensor([0.0024])\n",
-      "ace  =  tensor(0.0224)\n",
-      "tace  =  tensor(0.0110)\n"
+      "ece  =  tensor([0.0077])\n",
+      "sce  =  tensor([0.0014])\n",
+      "ace  =  tensor(0.0152)\n",
+      "tace  =  tensor(0.0074)\n"
      ]
     }
    ],
@@ -549,21 +543,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 102,
-   "metadata": {},
+   "execution_count": 64,
+   "metadata": {
+    "scrolled": true
+   },
    "outputs": [
     {
      "data": {
       "text/plain": [
        "Parameter containing:\n",
-       "tensor([ 1.0942e+00,  1.0579e+00,  1.0807e+00,  1.0858e+00,  1.1143e+00,\n",
-       "         1.0998e+00,  1.0911e+00,  1.1073e+00,  1.0508e+00,  1.1783e+00,\n",
-       "        -9.8967e-04,  1.2546e-03, -7.5154e-03,  7.0824e-03,  2.1402e-03,\n",
-       "        -1.2270e-02, -2.2263e-03,  9.1528e-03, -1.4546e-02,  1.7918e-02],\n",
-       "       requires_grad=True)"
+       "tensor([ 1.0551,  1.0509,  1.1472,  1.3279,  1.2181,  1.1756,  1.3048,  1.2188,\n",
+       "         1.4252,  1.2829, -0.0386, -0.0513, -0.0233,  0.0380, -0.0419, -0.0182,\n",
+       "         0.0301, -0.0224,  0.1063,  0.0213], requires_grad=True)"
       ]
      },
-     "execution_count": 102,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -574,7 +568,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 103,
+   "execution_count": 65,
    "metadata": {},
    "outputs": [
     {
@@ -599,39 +593,41 @@
        ")"
       ]
      },
-     "execution_count": 103,
+     "execution_count": 65,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "calibr = calibrator.ModelWithMatrScaling(model, logits, labels).float()\n",
-    "calibr.scaling(lr=0.0001, max_iter=1000)"
+    "calibr = calibrator.ModelWithMatrScaling(model, n_classes=10).float()\n",
+    "calibr.scaling(logits, labels, lr=0.0001, max_iter=1000)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 104,
+   "execution_count": 66,
    "metadata": {},
    "outputs": [],
    "source": [
-    "matr_scaling_logits = calibr.scaling_logits(val_logits)\n",
-    "matr_scaling_probs = f.softmax(matr_scaling_logits, dim=1)"
+    "matr_scaling_probs_list = []\n",
+    "for x_batch, y_batch in val_loader:\n",
+    "    matr_scaling_probs_list.append(calibr.forward(x_batch))\n",
+    "matr_scaling_probs = torch.cat(matr_scaling_probs_list)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 105,
+   "execution_count": 67,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "ece  =  tensor([0.0051])\n",
+      "ece  =  tensor([0.0056])\n",
       "sce  =  tensor([0.0014])\n",
-      "ace  =  tensor(0.0167)\n",
-      "tace  =  tensor(0.0061)\n"
+      "ace  =  tensor(0.0149)\n",
+      "tace  =  tensor(0.0066)\n"
      ]
     }
    ],
@@ -642,7 +638,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 106,
+   "execution_count": 68,
    "metadata": {
     "scrolled": true
    },
@@ -653,17 +649,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 108,
+   "execution_count": 69,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "ece  =  tensor([0.0069])\n",
-      "sce  =  tensor([0.0016])\n",
-      "ace  =  tensor(0.0177, dtype=torch.float64)\n",
-      "tace  =  tensor(0.0129, dtype=torch.float64)\n"
+      "ece  =  tensor([0.0077])\n",
+      "sce  =  tensor([0.0015])\n",
+      "ace  =  tensor(0.0145, dtype=torch.float64)\n",
+      "tace  =  tensor(0.0105, dtype=torch.float64)\n"
      ]
     }
    ],
@@ -671,6 +667,13 @@
     "compute_errors(n_bins=15, probs=hist_binning_probs, labels=val_labels.numpy(),\n",
     "               len_dataset=np.shape(probs)[0], threshold=0.9)"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
@@ -695,7 +698,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.4"
+   "version": "3.7.6"
   },
   "widgets": {
    "application/vnd.jupyter.widget-state+json": {
@@ -1242,11 +1245,11 @@
       "description": " 93%",
       "description_tooltip": null,
       "layout": "IPY_MODEL_c5fbb54c30174247a4b890e22a96cd15",
-      "max": 50000.0,
-      "min": 0.0,
+      "max": 50000,
+      "min": 0,
       "orientation": "horizontal",
       "style": "IPY_MODEL_f95b3d10c84f400faa38c4396870d859",
-      "value": 46587.0
+      "value": 46587
      }
     },
     "3f677cdc4469460c852fe4d9a6979869": {
@@ -1438,11 +1441,11 @@
       "description": "Extraction completed...: 100%",
       "description_tooltip": null,
       "layout": "IPY_MODEL_b6689d61d6604d8981d446c538fbd44f",
-      "max": 1.0,
-      "min": 0.0,
+      "max": 1,
+      "min": 0,
       "orientation": "horizontal",
       "style": "IPY_MODEL_de3041298f1e496d93a8d58259cd7009",
-      "value": 1.0
+      "value": 1
      }
     },
     "547d771bf7d146a19ef02a463c28a496": {
@@ -1595,11 +1598,11 @@
       "description": "",
       "description_tooltip": null,
       "layout": "IPY_MODEL_05f0a259a8d643c1ae85ecde57be4981",
-      "max": 1.0,
-      "min": 0.0,
+      "max": 1,
+      "min": 0,
       "orientation": "horizontal",
       "style": "IPY_MODEL_fb2bc264a3ae41028b3d7bcabdfcc009",
-      "value": 1.0
+      "value": 1
      }
     },
     "8cf16a3e63e3413a9b873711757595d0": {
@@ -1632,11 +1635,11 @@
       "description": "Dl Completed...: 100%",
       "description_tooltip": null,
       "layout": "IPY_MODEL_94fe1defabd84e3a8d31f398aeaf1455",
-      "max": 1.0,
-      "min": 0.0,
+      "max": 1,
+      "min": 0,
       "orientation": "horizontal",
       "style": "IPY_MODEL_c2c2b28ffcae4bf29973bb229a663da3",
-      "value": 1.0
+      "value": 1
      }
     },
     "9263135419074499a42e519958ed514a": {
@@ -2043,11 +2046,11 @@
       "description": "Dl Size...: 100%",
       "description_tooltip": null,
       "layout": "IPY_MODEL_9263135419074499a42e519958ed514a",
-      "max": 1.0,
-      "min": 0.0,
+      "max": 1,
+      "min": 0,
       "orientation": "horizontal",
       "style": "IPY_MODEL_23306e469c1342b9921883cf33502298",
-      "value": 1.0
+      "value": 1
      }
     },
     "c2c2b28ffcae4bf29973bb229a663da3": {
@@ -2146,11 +2149,11 @@
       "description": "",
       "description_tooltip": null,
       "layout": "IPY_MODEL_a4bc6f0e24fb4242b5536d0906810dc1",
-      "max": 1.0,
-      "min": 0.0,
+      "max": 1,
+      "min": 0,
       "orientation": "horizontal",
       "style": "IPY_MODEL_59f6ddd1dfcb445a8fa9f2cc9a9eaf8b",
-      "value": 1.0
+      "value": 1
      }
     },
     "d416605b18cc46658e89c1d4cb42fe46": {
@@ -2169,11 +2172,11 @@
       "description": "  0%",
       "description_tooltip": null,
       "layout": "IPY_MODEL_f7f30d82a72146be891adeb94eeabfc3",
-      "max": 10000.0,
-      "min": 0.0,
+      "max": 10000,
+      "min": 0,
       "orientation": "horizontal",
       "style": "IPY_MODEL_29afad3a94774993a0f437e4ac2f9e2a",
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From ef8624a061cd7bad7ec0a4f472c90cc7c5270e54 Mon Sep 17 00:00:00 2001
From: mtereshkin <63161001+mtereshkin@users.noreply.github.com>
Date: Sat, 19 Sep 2020 19:06:36 +0300
Subject: [PATCH 8/8] Delete old version of calibrator.py

---
 examples/calibrator.py | 211 -----------------------------------------
 1 file changed, 211 deletions(-)
 delete mode 100644 examples/calibrator.py

diff --git a/examples/calibrator.py b/examples/calibrator.py
deleted file mode 100644
index 03d038d..0000000
--- a/examples/calibrator.py
+++ /dev/null
@@ -1,211 +0,0 @@
-import sklearn
-import numpy as np
-
-import math
-from torch.nn import functional as f
-import torch
-from torch import nn, optim
-import math
-from scipy.special import softmax
-
-
-class Calibrator():
-    def __init__(self, logits, labels):
-        self.temperature = torch.ones(1, requires_grad=True)
-        self.logits = logits
-        self.labels = labels
-        self.W = torch.diag(torch.ones(logits.shape[1]))
-        self.W.requires_grad_()
-        self.b = torch.zeros(logits.shape[1], requires_grad=True)
-        self.W_diag = torch.cat((torch.ones(logits.shape[1]), torch.zeros(logits.shape[1])), dim=0)
-        self.W_diag.requires_grad_()
-
-    def split_into_bins(self, n_bins, logits, labels):
-        bins = []
-        true_labels_for_bins = []
-
-        for i in range(n_bins):
-            bins.append([])
-            true_labels_for_bins.append([])
-
-        for j in range(len(labels)):
-            max_p = max(softmax(logits[j]))
-            for i in range(n_bins):
-                if i / n_bins < max_p and max_p <= (i + 1) / n_bins:
-                    bins[i].append((logits[j]))
-                    true_labels_for_bins[i].append(labels[j])
-        return np.array(bins), np.array(true_labels_for_bins)
-
-    def compute_ece(self, n_bins, logits, labels, len_dataset):
-        bins, true_labels_for_bins = self.split_into_bins(n_bins, logits, labels)
-        bins = list(filter(None, bins))
-        true_labels_for_bins = list(filter(None, true_labels_for_bins))
-        ece = torch.zeros(1)
-        for i in range(len(bins)):
-            softmaxes = f.softmax(torch.from_numpy(np.array(bins[i])), dim=1)
-            confidences, predictions = torch.max(softmaxes, dim=1)
-            accuracy = sklearn.metrics.accuracy_score(true_labels_for_bins[i], predictions)
-            confidence = torch.sum(confidences) / len(bins[i])
-            ece += len(bins[i]) * torch.abs(accuracy - confidence) / len_dataset
-        return ece
-
-    def split_into_classes(self, dataset, column_label, logits):
-        by_column = dataset.groupby(column_label)
-        datasets = {}
-        class_logits = []
-        dict_class_logits = {}
-        n_classes = len(set(dataset[column_label]))
-        for i in range(n_classes):
-            class_logits.append([])
-        for groups, data in by_column:
-            datasets[groups] = data
-        for ind, label in enumerate(dataset[column_label].to_numpy()):
-            for i in range(n_classes):
-                if label == i:
-                    class_logits[i].append(logits[ind])
-        for i in range(n_classes):
-            dict_class_logits[i] = class_logits[i]
-        return datasets, dict_class_logits
-
-    def compute_sce(self, nbins, column_label, logits, dataset):
-        ece_values_for_each_class = []
-        datasets, dict_class_logits = self.split_into_classes(dataset, column_label, logits)
-        for item in datasets.keys():
-            ece_values_for_each_class.append(
-                self.compute_ece(nbins, dict_class_logits[item], datasets[item][column_label].to_numpy(), len(dataset)))
-        return sum(ece_values_for_each_class) / len(datasets.keys())
-
-    def SplitIntoRanges(self, R, logits, labels):
-        N = len(logits)
-        bins = []
-        true_labels = []
-        for i in range(R):
-            bins.append([])
-            true_labels.append([])
-        for j in range(R):
-            for i in range(j * math.floor(N / R), (j + 1) * math.floor(N / R)):
-                bins[j].append(logits[i])
-                true_labels[j].append(labels[i])
-        return np.array(bins), np.array(true_labels)
-
-    def ComputeAce(self, R, dataset, target, logits):
-        datasets, dict_class_logits = self.split_into_classes(dataset, target, logits)
-        summa = 0
-        for dataset in datasets.keys():
-            data = datasets[dataset]
-            class_labels = data[target].to_numpy()
-            class_logits = dict_class_logits[dataset]
-            bins, true_labels = self.SplitIntoRanges(R, class_logits, class_labels)
-            for binn, bin_labels in zip(bins, true_labels):
-                softmaxes = f.softmax(torch.from_numpy(binn), dim=1)
-                accuracy = sklearn.metrics.accuracy_score(torch.from_numpy(bin_labels), np.argmax(softmaxes, axis=1))
-                conf_array = torch.max(softmaxes, dim=1)[0]
-                confidence = torch.sum(conf_array) / len(conf_array)
-                substraction = abs(accuracy - confidence)
-                summa += substraction
-        ACE = summa / (len(datasets.keys()) * R)
-        return ACE
-
-    def ChooseData(self, threshold, dataset, logits):
-        arr = torch.max(f.softmax(torch.from_numpy(logits), dim=1), dim=1)[0]
-        arr.numpy()
-        arr_with_indices = list(enumerate(arr))
-        arr_with_indices.sort(key=lambda x: x[1])
-        thr_array = []
-        for pair in arr_with_indices:
-            if pair[1] > threshold:
-                thr_array.append(pair)
-        indices = []
-        for pair in thr_array:
-            indices.append(pair[0])
-        chosen_data = dataset.iloc[indices]
-        chosen_logits = logits[indices]
-        return chosen_data, chosen_logits
-
-    def ComputeTace(self, threshold, dataset, logits, R, target):
-        chosen_data, chosen_logits = self.ChooseData(threshold, dataset, logits)
-        return self.ComputeAce(R, chosen_data, target, chosen_logits)
-
-    def NumberOfClasses(self, dataset, target):
-        by_column = dataset.groupby(target)
-        datasets = {}
-        for groups, data in by_column:
-            datasets[groups] = data
-        return len(datasets)
-
-    def matrix_scaling_logits(self, logits):
-        self.b.unsqueeze(0).expand(logits.shape[0], -1)
-        return torch.mm(torch.from_numpy(logits), self.W) + self.b
-
-    def vector_scaling_logits(self, logits):
-        W = torch.diag(self.W_diag[:logits.shape[1]])
-        b = self.W_diag[logits.shape[1]:]
-        b = b.unsqueeze(0).expand(logits.shape[0], -1)
-        return torch.mm(torch.from_numpy(logits), W) + b
-
-    def scale_logits_with_temperature(self, logits):
-        self.temperature.unsqueeze(1).expand(logits.shape[0], logits.shape[1])
-        return torch.true_divide(torch.from_numpy(logits), self.temperature)
-
-    def TemperatureScaling(self):
-        nll = nn.CrossEntropyLoss()
-        optimizer = optim.LBFGS([self.temperature], lr=0.0001, max_iter=500)
-
-        def eval():
-            loss = nll(self.scale_logits_with_temperature(self.logits), torch.from_numpy(np.array(self.labels)))
-            loss.backward()
-            return loss
-
-        optimizer.step(eval)
-        return self
-
-    def MatrixScaling(self):
-
-        nll = nn.CrossEntropyLoss()
-        optimizer = optim.LBFGS([self.W, self.b], lr=0.0001, max_iter=1000)
-
-        def eval():
-            loss = nll(self.matrix_scaling_logits(self.logits), torch.from_numpy(np.array(self.labels)))
-            loss.backward()
-            return loss
-
-        optimizer.step(eval)
-        return self
-
-    def VectorScaling(self):
-        nll = nn.CrossEntropyLoss()
-        optimizer = optim.LBFGS([self.W_diag], lr=0.000001, max_iter=9000)
-
-        def eval():
-            loss = nll(self.vector_scaling_logits(self.logits), torch.from_numpy(np.array(self.labels)))
-            loss.backward()
-            return loss
-
-        optimizer.step(eval)
-        return self
-
-
-def binary_histogram_binning(num_bins, probs, labels, probs_to_calibrate):
-    bins = np.linspace(0, 1, num=num_bins)
-    indexes_list = np.digitize(probs, bins) - 1
-    theta = np.zeros(num_bins)
-    for i in range(len(bins)):
-        binn = (indexes_list == i)
-        binn_len = np.sum(binn)
-        if binn_len != 0:
-            theta[i] = np.sum(labels[binn]) / binn_len
-        else:
-            theta[i] = bins[i]
-    return list(map(lambda x: theta[np.digitize(x, bins) - 1], probs_to_calibrate))
-
-
-def multiclass_histogram_binning(num_bins, logits, labels, logits_to_calibrate):
-    probs = softmax(logits, axis=1)
-    probs_to_calibrate = softmax(logits_to_calibrate, axis=1)
-    binning_res = []
-    for k in range(np.shape(probs)[1]):
-        binning_res.append(binary_histogram_binning(num_bins, probs[:, k], labels == k, probs_to_calibrate[:, k]))
-    binning_res = np.vstack(binning_res).T
-    cal_confs = binning_res / (np.sum(binning_res, axis=1)[:, None])
-    return cal_confs
-