ia tp5

ia/tp5/.gitignore

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+/venv

ia/tp5/questions.md

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+# Questions TP5 d'IA
+
+> Matthieu Jolimaitre
+
+## Partie 1
+
+### 1. D’après le modèle ajusté, quelle est la température attendue si la puissance est de 120W ?
+
+```
+f(120) = 64.61248085407703
+```
+
+ce qui implique que la température attendue si la puissance est de 120W est de
+64.61°.
+
+### 2. Que vaut la RMSE et quelle est son unité ?
+
+```
+RMSE = 5.662048552655999
+```
+
+L'unité de la RMSE est un écart de températures en degrés.
+
+### 3. Quelle est la valeur de température qui admet la plus grande erreur d’approximation ?
+
+```
+Maximal error = 14.337368012120734
+for (x, y) = (153.89061334817407, 91.90827168300679)
+```
+
+La valeur de température qui admet la plus grande erreur d'approximation est de
+91.91° pour une puissance de 153.89W.
+
+### 4. Le modèle est-il meilleur ou moins bon que sur le jeu de données précédent ? Pour quelle raison ce modèle est, ou n’est pas, adapté à ces données ?
+
+```
+f(120) = 44.42433903389104
+RMSE = 13.428963137234206
+Maximal error = 47.681726938444285
+for (x, y) = (179.85011085382266, 113.05473219321803)
+```
+
+Le modèle est moins bon que sur le jeu de données précédent. En effet, la RMSE
+est plus élevée. Le modèle n'est pas adapté à ces données car il ne suit pas la
+tendance des données qui semble être parabolique ou exponentielle plutôt que
+linéaire.
+
+## Partie 2
+
+#### 5. En combien d’epochs le perceptron converge-t-il ?
+
+```
+M=1, score=0.966
+M=2, score=0.974
+M=3, score=1.0
+```
+
+Le perceptron converge en 3 epochs.
+
+#### 6. En combien d’epochs le perceptron converge-t-il ?
+
+```
+...
+M=1, score=0.908
+M=2, score=0.922
+M=3, score=0.924
+M=4, score=0.916
+M=5, score=0.912
+M=6, score=0.93
+...
+```
+
+Le perceptron semble converger en 5 epochs avant de regresser.
+
+#### 7. Que valent ces métriques avec ce nouveaux jeu de données avec 𝑀 = 25 epochs et un pas d’apprentissage 𝜌 = 0.01 ? Que vaut la loss définie par l’Equation 3 qui est minimisée par le Perceptron ?
+
+```
+precision = 0.9766666666666667
+recall = 0.8987730061349694
+F1 = 0.4680511182108626
+```
+
+```
+loss = 40
+```
+
+Le perceptron n'a pas pu converger d'avantage et a atteint une loss de 40. Ce
+qui signifie que 40 individus ont été mal classifiés.

ia/tp5/requirements.txt

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+numpy
+matplotlib

ia/tp5/setup.sh

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+#!/bin/sh
+cd "$(dirname "$(realpath "$0")")"
+
+python3 -m venv venv
+source venv/bin/activate
+
+pip install -r requirements.txt

ia/tp5/src/ex1_regression1.py

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+#!/usr/bin/env python3
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+x = np.array([107.01819675010165,142.97461762841453,128.3592388893137,178.48859894769942,105.07512391405761,133.9662346986653,106.88633746415002,165.9304901016704,175.27615886513382,99.8473974473511,152.9242549507464,63.265825397243646,77.1539782923285,170.32756297804593,59.2346875657253,61.32680896120029,52.62839166724234,158.24057992123193,151.16037762348054,163.1015792720865,177.22038449025933,153.89061334817407,109.99231709288114,151.46879291723923,65.37567536296132,133.1897327725781,68.63592736317604,172.8069592164459,70.97023732504951,103.90605219876807,84.3922295736015,150.65037962644817,109.29954318815132,134.9040823105018,52.44267405672617,130.29261461986403,129.57244395391479,130.2014195937184,172.68725020690113,138.63663888345286,96.73602707459219,106.81415399391439,140.69205547054443,57.82931131180508,136.6796730079368,137.18292305036073,77.34973293959932,66.76041869513094,91.00568562014391,97.28240022254093,])
+y = np.array([58.604012802664876,61.568938988109096,63.9339339649278,82.30116210624541,60.16795400802,64.93076361223594,58.199364484080114,78.94874665221919,96.59629220870175,55.08553593594234,80.59085994712159,42.765533811305836,51.2101273466327,89.89235901983224,40.98731129137799,41.45808065513656,38.63780451473805,73.0967722436298,71.29285705472836,79.97576728127771,92.61811453529036,91.90827168300679,61.526181495163584,63.194648094263655,43.7942773055833,64.14802974784072,44.56028490073529,89.47188535978337,44.40026349403853,59.98046502154318,48.28512591278614,84.23051603949706,62.02917662565915,62.1335255880633,38.81183960757261,62.94408352854921,79.54097547379997,77.90871790408256,71.16968980369258,74.30802693800463,55.39297558330232,62.1570061057422,75.8196079986226,41.200254600443635,77.03603317805609,67.24949240498717,50.174757752678055,43.80774399266216,56.51718964090277,56.610351455109445,])
+N = len(x)
+
+#
+# step 01
+#
+# - build data matrix X
+# - compute optimal w
+#
+
+X = np.ones((N, 2))
+X[:, 1] = x
+
+w = np.linalg.inv(X.T @ X) @ X.T @ y
+
+# 
+# step 02
+# 
+# - plot the model as a line y = w0 + w1 * x s
+#
+plt.figure()
+plt.scatter(x, y)
+
+x_min = np.min(x)
+x_max = np.max(x)
+x_plot = np.linspace(x_min, x_max, 100)
+y_plot = w[0] + w[1] * x_plot
+plt.plot(x_plot, y_plot, color='orange')
+
+# 
+# step 03
+# 
+# - predict new value f(x)
+# - compute RMSE
+# - compute maximal error
+#
+
+prediction = w[0] + w[1] * 120
+print(f'f(120) = {prediction}')
+
+y_pred = X @ w
+rmse = np.sqrt(np.sum((y - y_pred) ** 2) / N)
+print(f'RMSE = {rmse}')
+
+idx = np.argmax(np.abs(y - y_pred))
+max_error = np.abs(y[idx] - y_pred[idx])
+print(f'Maximal error = {max_error}')
+print(f'for (x, y) = ({x[idx]}, {y[idx]})')
+
+plt.show()

ia/tp5/src/ex1_regression2.py

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+#!/usr/bin/env python3
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+x = np.array([140.02910671010955,144.28305637655325,115.17216965047129,174.2908725140191,133.71872589985287,105.10115631256336,128.83111783663017,52.49511578021336,89.2047261676914,135.82255987404903,87.71008893735774,130.3420057698494,105.7399311229496,67.61162834891853,88.776702374284,124.09543839116444,126.81345896226252,124.66228235044524,134.91610658142736,134.77342510021955,106.08439660641662,166.5510574606382,97.78304310622656,106.66244028453148,165.95003615203737,154.80521857599115,141.5055158602476,63.02949535059915,169.53273978680755,142.85136894138446,179.85011085382266,69.42827960553919,162.85638745786787,71.12408150792874,130.02274335689975,66.0965977704274,160.24106981189047,154.9514646342514,123.98309601989713,102.93382863937995,58.991709409167946,140.66574050879328,108.96054874814895,143.86722793114524,162.6297023707218,176.81779565037516,161.25443451103945,51.522830944050256,96.7971483821873,144.89877311512754,])
+y = np.array([42.81605146528971,36.28330545155218,31.68572329595792,76.93511586659231,39.67091689151953,36.75433594698061,43.668607504626735,35.36147584081617,37.15391917695597,54.600834054029775,39.53711133759362,40.70788477452493,31.238140682578088,32.803846883928486,33.26497225482958,32.23737408256554,26.644077012420333,35.07966603555466,27.18589689633954,34.824784598255725,30.995750167590458,87.49142265447308,35.718581012669205,32.94444212403231,89.28741953891095,38.377360047677826,47.934251797831806,33.86693859748784,72.15159937429533,52.39883472306155,113.05473219321803,32.358600372044044,71.84653139192467,36.770050235085684,34.448886069864834,35.7827916825874,59.57702285934876,61.263901673061625,35.90307044444734,36.06547033199114,34.36729122240489,48.69663447942126,35.42784626944333,34.556197150504495,51.345881947334895,82.19073242621832,50.649674506375675,34.96619043312894,38.77250612852849,48.018188311243144,])
+N = len(x)
+
+# 
+# step 04
+# 
+
+
+X = np.ones((N, 2))
+X[:, 1] = x
+
+w = np.linalg.inv(X.T @ X) @ X.T @ y
+
+plt.figure()
+plt.scatter(x, y)
+
+x_min = np.min(x)
+x_max = np.max(x)
+x_plot = np.linspace(x_min, x_max, 100)
+y_plot = w[0] + w[1] * x_plot
+plt.plot(x_plot, y_plot, color='orange')
+
+prediction = w[0] + w[1] * 120
+print(f'f(120) = {prediction}')
+
+y_pred = X @ w
+rmse = np.sqrt(np.sum((y - y_pred) ** 2) / N)
+print(f'RMSE = {rmse}')
+
+idx = np.argmax(np.abs(y - y_pred))
+max_error = np.abs(y[idx] - y_pred[idx])
+print(f'Maximal error = {max_error}')
+print(f'for (x, y) = ({x[idx]}, {y[idx]})')
+
+plt.show()