problem.ipynb 62.5 KB
Newer Older
Mathilde Rineau's avatar
Mathilde Rineau committed
1
2
3
4
5
6
7
{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "5c8980bd",
   "metadata": {},
   "source": [
Rémy Huet's avatar
Rémy Huet committed
8
9
    "# AOS1 - Assignment\n",
    "## Improving the accuracy and speed of support vector machines\n",
Mathilde Rineau's avatar
Mathilde Rineau committed
10
    "\n",
Rémy Huet's avatar
Rémy Huet committed
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
    "Authors : Mathilde Rineau, Rémy Huet\n",
    "\n",
    "### Abstract\n",
    "\n",
    "The paper \"Improving the Accuracy and Speed of Support Vector Machines\" by Burges and Schölkopf is investigating a method to improve ht speed an accuracy of a support vector machine.\n",
    "\n",
    "As the authors say, SVM are wildly used for several applications.\n",
    "To improve this method, the authors make the difference between two types of improvements to achieve :\n",
    "- improving the generalization performance;\n",
    "- improving the speed in test phase.\n",
    "\n",
    "The authors propose and combine two methods to improve SVM performances : the \"virtual support vector\" method and the \"reduced set\" method.\n",
    "With those two improvements, they announce a machine much faster (22 times than the original one) and more precise (1.1% vs 1.4% error) than the original one.\n",
    "\n",
    "In this work, we will describe and program the two techniques they are used to see if these method are working as they say."
Mathilde Rineau's avatar
Mathilde Rineau committed
26
27
   ]
  },
Rémy Huet's avatar
Rémy Huet committed
28
29
  {
   "cell_type": "markdown",
Mathilde Rineau's avatar
Mathilde Rineau committed
30
   "id": "12aaeba6",
Rémy Huet's avatar
Rémy Huet committed
31
32
33
34
35
   "metadata": {},
   "source": [
    "### First part : tests with a vanilla SVM\n",
    "\n",
    "In this first part, we will use a vanilla SVM on the MINST dataset with the provided params.\n",
Mathilde Rineau's avatar
Mathilde Rineau committed
36
    "We will observe the error of the SVM and the time for the test phase to compare them with the improved version"
Rémy Huet's avatar
Rémy Huet committed
37
38
   ]
  },
Mathilde Rineau's avatar
Mathilde Rineau committed
39
40
  {
   "cell_type": "code",
Rémy Huet's avatar
Rémy Huet committed
41
   "execution_count": 1,
Mathilde Rineau's avatar
Mathilde Rineau committed
42
43
   "id": "9f152334",
   "metadata": {},
Rémy Huet's avatar
Rémy Huet committed
44
   "outputs": [],
Mathilde Rineau's avatar
Mathilde Rineau committed
45
   "source": [
Rémy Huet's avatar
Rémy Huet committed
46
47
    "# We will work on the mnist data set\n",
    "# We load it from fetch_openml\n",
Mathilde Rineau's avatar
Mathilde Rineau committed
48
49
    "from sklearn.datasets import fetch_openml\n",
    "import matplotlib.pyplot as plt\n",
Rémy Huet's avatar
Rémy Huet committed
50
    "import numpy as np\n",
Mathilde Rineau's avatar
Mathilde Rineau committed
51
    "\n",
Rémy Huet's avatar
Rémy Huet committed
52
53
54
55
56
    "X, y = fetch_openml('mnist_784', version=1, return_X_y=True, as_frame=False)"
   ]
  },
  {
   "cell_type": "markdown",
Mathilde Rineau's avatar
Mathilde Rineau committed
57
   "id": "855cdb06",
Rémy Huet's avatar
Rémy Huet committed
58
59
60
61
62
63
64
   "metadata": {},
   "source": [
    "We do some inspection on the dataset :"
   ]
  },
  {
   "cell_type": "code",
Rémy Huet's avatar
Rémy Huet committed
65
   "execution_count": 2,
Mathilde Rineau's avatar
Mathilde Rineau committed
66
   "id": "708c8ea1",
Rémy Huet's avatar
Rémy Huet committed
67
   "metadata": {},
Rémy Huet's avatar
Rémy Huet committed
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(70000, 784)\n",
      "(70000,)\n",
      "['0' '1' '2' '3' '4' '5' '6' '7' '8' '9']\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7fd08176bfd0>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
Rémy Huet's avatar
Rémy Huet committed
101
102
   "source": [
    "# We print the caracteristics of X and Y\n",
Mathilde Rineau's avatar
Mathilde Rineau committed
103
    "print(X.shape)\n",
Rémy Huet's avatar
Rémy Huet committed
104
105
106
107
108
109
110
111
112
113
    "print(y.shape)\n",
    "# Values taken by y\n",
    "print(np.unique(y))\n",
    "\n",
    "image = np.reshape(X[0], (28, 28))\n",
    "plt.imshow(image, cmap='gray')"
   ]
  },
  {
   "cell_type": "markdown",
Mathilde Rineau's avatar
Mathilde Rineau committed
114
   "id": "4e49be54",
Rémy Huet's avatar
Rémy Huet committed
115
116
117
118
119
120
121
122
123
124
125
126
   "metadata": {},
   "source": [
    "The dataset contains 70k samples of 784 features.\n",
    "The classes are 0 to 9 (the digits on the images).\n",
    "\n",
    "The features are the pixels of a 28 x 28 image that we can retrieve using numpy's reshape function.\n",
    "\n",
    "For example, the 1st image is a 5."
   ]
  },
  {
   "cell_type": "markdown",
Mathilde Rineau's avatar
Mathilde Rineau committed
127
   "id": "60f31892",
Rémy Huet's avatar
Rémy Huet committed
128
129
130
131
132
133
   "metadata": {},
   "source": [
    "With our dataset, we can generate a training dataset and a testing dataset.\n",
    "As in the article, we will use 60k samples as training samples and 10k as testing.\n",
    "\n",
    "We split the dataset using the `train_test_split` function from `sklearn`."
Mathilde Rineau's avatar
Mathilde Rineau committed
134
135
136
137
   ]
  },
  {
   "cell_type": "code",
Rémy Huet's avatar
Rémy Huet committed
138
   "execution_count": 3,
Mathilde Rineau's avatar
Mathilde Rineau committed
139
140
141
142
   "id": "4d3fa1c7",
   "metadata": {},
   "outputs": [],
   "source": [
Rémy Huet's avatar
Rémy Huet committed
143
144
    "# We divide the data set in two parts: train set and test set\n",
    "# According to the recommended values the train set's size is 60000 and the test set's size is 10000\n",
Mathilde Rineau's avatar
Mathilde Rineau committed
145
146
147
148
149
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "    X, y, train_size=60000, test_size=10000)"
   ]
  },
Rémy Huet's avatar
Rémy Huet committed
150
151
  {
   "cell_type": "markdown",
Mathilde Rineau's avatar
Mathilde Rineau committed
152
   "id": "d0532cc1",
Rémy Huet's avatar
Rémy Huet committed
153
154
155
156
157
158
159
160
161
   "metadata": {},
   "source": [
    "From the article, we retrieve the parameters of the SVM used.\n",
    "We get C = 10, and a polynomial kernel of degree 5.\n",
    "Coefficients `gamma` and `coef0` are respectively equals to 1 and 0.\n",
    "\n",
    "We can now train a SVM with these params on the training dataset."
   ]
  },
Mathilde Rineau's avatar
Mathilde Rineau committed
162
163
  {
   "cell_type": "code",
Rémy Huet's avatar
Rémy Huet committed
164
   "execution_count": 4,
Mathilde Rineau's avatar
Mathilde Rineau committed
165
166
   "id": "d809fc87",
   "metadata": {},
Rémy Huet's avatar
Rémy Huet committed
167
168
169
170
171
172
173
174
175
176
177
178
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVC(C=10, coef0=0, degree=5, gamma=1, kernel='poly')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
Mathilde Rineau's avatar
Mathilde Rineau committed
179
   "source": [
Rémy Huet's avatar
Rémy Huet committed
180
    "# First, we perform a SVC without preprocessing or improving in terms of accuracy or speed\n",
Mathilde Rineau's avatar
Mathilde Rineau committed
181
    "from sklearn.svm import SVC\n",
Rémy Huet's avatar
Rémy Huet committed
182
183
184
    "# we perform the default SVC, with the hyperparameter C=10 and a polynomial kernel of degree 5\n",
    "# according to the recommandations\n",
    "svc = SVC(C=10, kernel = 'poly', degree = 5, gamma=1, coef0=0)\n",
Mathilde Rineau's avatar
Mathilde Rineau committed
185
186
187
    "svc.fit(X_train, y_train)"
   ]
  },
Rémy Huet's avatar
Rémy Huet committed
188
189
  {
   "cell_type": "markdown",
Mathilde Rineau's avatar
Mathilde Rineau committed
190
   "id": "a8cf4850",
Rémy Huet's avatar
Rémy Huet committed
191
192
193
194
195
196
197
198
   "metadata": {},
   "source": [
    "Using the previously trained SVM, we make a prediction on the test dataset.\n",
    "\n",
    "One of the measured performance of the SVM in this article is the speed of the test phase.\n",
    "We thus measure it."
   ]
  },
Mathilde Rineau's avatar
Mathilde Rineau committed
199
200
  {
   "cell_type": "code",
Rémy Huet's avatar
Rémy Huet committed
201
   "execution_count": 5,
Mathilde Rineau's avatar
Mathilde Rineau committed
202
203
   "id": "8cb28178",
   "metadata": {},
Rémy Huet's avatar
Rémy Huet committed
204
205
206
207
208
209
210
211
212
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elapsed time : 81.90112400054932\n"
     ]
    }
   ],
Mathilde Rineau's avatar
Mathilde Rineau committed
213
   "source": [
Rémy Huet's avatar
Rémy Huet committed
214
215
216
217
218
219
220
221
222
223
224
225
226
227
    "import time\n",
    "\n",
    "start = time.time()\n",
    "# We predict the values for our test set\n",
    "y_pred = svc.predict(X_test)\n",
    "end = time.time()\n",
    "\n",
    "# We predict 10 times to have a mean elapsed time\n",
    "\n",
    "print(f'Elapsed time : {end - start}')"
   ]
  },
  {
   "cell_type": "markdown",
Mathilde Rineau's avatar
Mathilde Rineau committed
228
   "id": "90f08e8b",
Rémy Huet's avatar
Rémy Huet committed
229
230
   "metadata": {},
   "source": [
Rémy Huet's avatar
Rémy Huet committed
231
    "Of course the prediction time varies between two splits of the dataset, two computers and two executions, but we will retain that is is close from 70s.\n",
Rémy Huet's avatar
Rémy Huet committed
232
233
    "\n",
    "Using `y_test` the real classes of the `X_test` samples and `y_pred` the predicted classes from the SVM, we can compute the confusion matrix and the error to see the how good the predictions are."
Mathilde Rineau's avatar
Mathilde Rineau committed
234
235
236
237
   ]
  },
  {
   "cell_type": "code",
Rémy Huet's avatar
Rémy Huet committed
238
   "execution_count": 6,
Mathilde Rineau's avatar
Mathilde Rineau committed
239
240
   "id": "c1248238",
   "metadata": {},
Rémy Huet's avatar
Rémy Huet committed
241
242
243
244
245
246
247
248
249
250
251
252
253
254
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
Mathilde Rineau's avatar
Mathilde Rineau committed
255
   "source": [
Rémy Huet's avatar
Rémy Huet committed
256
257
258
259
260
261
    "# We compute the confusion matrix\n",
    "from sklearn.metrics import ConfusionMatrixDisplay, classification_report, accuracy_score\n",
    "\n",
    "disp = ConfusionMatrixDisplay.from_predictions(y_test, y_pred)\n",
    "disp.figure_.suptitle('Confusion matrix for the vanilla SVM')\n",
    "plt.show()"
Mathilde Rineau's avatar
Mathilde Rineau committed
262
263
264
265
   ]
  },
  {
   "cell_type": "code",
Rémy Huet's avatar
Rémy Huet committed
266
   "execution_count": 7,
Mathilde Rineau's avatar
Mathilde Rineau committed
267
268
   "id": "ba4e38ac",
   "metadata": {},
Rémy Huet's avatar
Rémy Huet committed
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              precision    recall  f1-score   support\n",
      "\n",
      "           0       0.96      0.99      0.97      1053\n",
      "           1       0.95      0.99      0.97      1145\n",
      "           2       0.98      0.96      0.97       988\n",
      "           3       0.97      0.96      0.96      1023\n",
      "           4       0.98      0.97      0.98       970\n",
      "           5       0.97      0.96      0.97       890\n",
      "           6       0.99      0.97      0.98       961\n",
      "           7       0.98      0.97      0.98      1015\n",
      "           8       0.96      0.96      0.96       980\n",
      "           9       0.98      0.96      0.97       975\n",
      "\n",
      "    accuracy                           0.97     10000\n",
      "   macro avg       0.97      0.97      0.97     10000\n",
      "weighted avg       0.97      0.97      0.97     10000\n",
      "\n"
     ]
    }
   ],
Mathilde Rineau's avatar
Mathilde Rineau committed
294
   "source": [
Rémy Huet's avatar
Rémy Huet committed
295
    "# We print the classification report\n",
Mathilde Rineau's avatar
Mathilde Rineau committed
296
297
298
299
300
    "print(classification_report(y_test, y_pred))"
   ]
  },
  {
   "cell_type": "code",
Rémy Huet's avatar
Rémy Huet committed
301
   "execution_count": 8,
Mathilde Rineau's avatar
Mathilde Rineau committed
302
303
   "id": "947b0895",
   "metadata": {},
Rémy Huet's avatar
Rémy Huet committed
304
305
306
307
308
309
310
311
312
313
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy:  0.9711\n",
      "Error rate:  2.8900000000000037 %\n"
     ]
    }
   ],
Mathilde Rineau's avatar
Mathilde Rineau committed
314
   "source": [
Rémy Huet's avatar
Rémy Huet committed
315
316
317
318
319
320
321
322
323
    "# We print the accuracy of the SVC and the error rate\n",
    "acc = accuracy_score(y_test, y_pred)\n",
    "\n",
    "print(\"Accuracy: \", acc)\n",
    "print(\"Error rate: \", (1-acc) * 100, \"%\")"
   ]
  },
  {
   "cell_type": "markdown",
Mathilde Rineau's avatar
Mathilde Rineau committed
324
   "id": "8f780139",
Rémy Huet's avatar
Rémy Huet committed
325
326
327
328
329
330
   "metadata": {},
   "source": [
    "As earlier, the values are affected by the selection of the training and testing dateset. Wi will retain a value of 3 % for the error.\n",
    "\n",
    "The method described py the authors relies on the support vectors of the previously trained SVM.\n",
    "We will thus do some inspection on them before going further."
Mathilde Rineau's avatar
Mathilde Rineau committed
331
332
333
334
   ]
  },
  {
   "cell_type": "code",
Rémy Huet's avatar
Rémy Huet committed
335
   "execution_count": 9,
Mathilde Rineau's avatar
Mathilde Rineau committed
336
337
   "id": "81b09df7",
   "metadata": {},
Rémy Huet's avatar
Rémy Huet committed
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(7425, 784)\n",
      "97\n",
      "0\n",
      "Class of the first support vector : 0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7fd06cbcbee0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
Mathilde Rineau's avatar
Mathilde Rineau committed
372
   "source": [
Rémy Huet's avatar
Rémy Huet committed
373
374
375
376
377
378
379
    "s_vects = svc.support_vectors_\n",
    "\n",
    "print(s_vects.shape)\n",
    "\n",
    "v = s_vects[0]\n",
    "v_index = svc.support_[0]\n",
    "v_class = y_train[v_index]\n",
Mathilde Rineau's avatar
Mathilde Rineau committed
380
381
    "print(v_index)\n",
    "print(v_class)\n",
Rémy Huet's avatar
Rémy Huet committed
382
383
384
385
386
387
388
389
    "\n",
    "print(f'Class of the first support vector : {v_class}')\n",
    "img = np.reshape(v, (28, 28))\n",
    "plt.imshow(img, cmap='gray')"
   ]
  },
  {
   "cell_type": "markdown",
Mathilde Rineau's avatar
Mathilde Rineau committed
390
   "id": "14cb2622",
Rémy Huet's avatar
Rémy Huet committed
391
392
393
394
395
396
397
398
399
   "metadata": {},
   "source": [
    "There are around 7500 support vectors in the SVM.\n",
    "\n",
    "Each support vector is a sample of `X_train`. We can thus retrieve its class using its index on the train dataset, and display it as an image as above."
   ]
  },
  {
   "cell_type": "markdown",
Mathilde Rineau's avatar
Mathilde Rineau committed
400
   "id": "fa1d441f",
Rémy Huet's avatar
Rémy Huet committed
401
402
   "metadata": {},
   "source": [
Rémy Huet's avatar
Rémy Huet committed
403
    "### Implementing the \"Virtual Support Vectors\" method\n",
Rémy Huet's avatar
Rémy Huet committed
404
    "\n",
Rémy Huet's avatar
Rémy Huet committed
405
406
407
408
409
410
411
412
413
    "We will now implement the \"Virtual Support Vectors\" as proposed by the authors.\n",
    "The aim of this method is to add some invariance in the data to make the previsions more robust.\n",
    "\n",
    "For a given trained SVM, we now that the only data relevant for classification are the support vectors.\n",
    "We will thus re-train a SVM, but with different data created from the support vectors.\n",
    "\n",
    "Here, the invariance proposed is shifting the image to one of the four directions.\n",
    "\n",
    "For each support vector, we will shift the image to the four directions, and use those images as a new dataset."
Rémy Huet's avatar
Rémy Huet committed
414
415
416
417
   ]
  },
  {
   "cell_type": "code",
Rémy Huet's avatar
Rémy Huet committed
418
   "execution_count": 16,
Rémy Huet's avatar
Rémy Huet committed
419
   "metadata": {},
Rémy Huet's avatar
Rémy Huet committed
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(29700, 784)\n",
      "(29700,)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7fd04f5f1d30>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
Rémy Huet's avatar
Rémy Huet committed
461
   "source": [
Rémy Huet's avatar
Rémy Huet committed
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
    "# Retrieve the indexes of the support vectors\n",
    "sv_indexes = svc.support_\n",
    "\n",
    "# Arrays for storing the data\n",
    "X_vsv = []\n",
    "y_vsv = []\n",
    "\n",
    "for i in sv_indexes:\n",
    "    # Get the support vector and reshape it as image\n",
    "    sv = X_train[i].reshape((28, 28))\n",
    "    sv_class = y_train[i]\n",
    "    # Generate the four shifts, reshape them\n",
    "    sv_1 = np.roll(sv, 1, axis=0).reshape(784)\n",
    "    sv_2 = np.roll(sv, -1, axis=0).reshape(784)\n",
    "    sv_3 = np.roll(sv, 1, axis=1).reshape(784)\n",
    "    sv_4 = np.roll(sv, -1, axis=1).reshape(784)\n",
    "\n",
    "    # Add them to the dataset\n",
    "    X_vsv.append(sv_1)\n",
    "    X_vsv.append(sv_2)\n",
    "    X_vsv.append(sv_3)\n",
    "    X_vsv.append(sv_4)\n",
    "\n",
    "    # Add the corresponding classes\n",
    "    y_vsv.append(sv_class)\n",
    "    y_vsv.append(sv_class)\n",
    "    y_vsv.append(sv_class)\n",
    "    y_vsv.append(sv_class)\n",
    "\n",
    "X_vsv = np.array(X_vsv)\n",
    "y_vsv = np.array(y_vsv)\n",
    "\n",
    "print(X_vsv.shape)\n",
    "print(y_vsv.shape)\n",
    "\n",
    "im0 = X_vsv[0].reshape((28, 28))\n",
    "im1 = X_vsv[1].reshape((28, 28))\n",
    "im2 = X_vsv[2].reshape((28, 28))\n",
    "im3 = X_vsv[3].reshape((28, 28))\n",
    "\n",
    "plt.figure()\n",
    "_, axis = plt.subplots(1, 4)\n",
    "axis[0].imshow(im0, cmap='gray')\n",
    "axis[1].imshow(im1, cmap='gray')\n",
    "axis[2].imshow(im2, cmap='gray')\n",
    "axis[3].imshow(im3, cmap='gray')"
Rémy Huet's avatar
Rémy Huet committed
508
   ]
Mathilde Rineau's avatar
Mathilde Rineau committed
509
510
511
  }
 ],
 "metadata": {
Rémy Huet's avatar
Rémy Huet committed
512
513
514
  "interpreter": {
   "hash": "78ff2a7d75990e26f7862f23aec114522929670ec71bbfd9a70bdb18a9100993"
  },
Mathilde Rineau's avatar
Mathilde Rineau committed
515
  "kernelspec": {
Rémy Huet's avatar
Rémy Huet committed
516
   "display_name": "Python 3.8.10 64-bit ('AOS1-3HAiNONq': pipenv)",
Mathilde Rineau's avatar
Mathilde Rineau committed
517
518
519
520
521
522
523
524
525
526
527
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
Mathilde Rineau's avatar
Mathilde Rineau committed
528
   "pygments_lexer": "ipython3",
Rémy Huet's avatar
Rémy Huet committed
529
   "version": "3.8.10"
Mathilde Rineau's avatar
Mathilde Rineau committed
530
531
532
533
534
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}