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Boston Dataset

Bibliothèques

Tout d'abord, exécutons la cellule ci-dessous pour importer tous les paquets dont vous aurez besoin au cours de cette étude.

  • pandas est une bibliothèque écrite pour le langage de programmation Python permettant la manipulation et l'analyse des données.

  • numpy est une bibliothèque pour langage de programmation Python, destinée à manipuler des matrices ou tableaux multidimensionnels ainsi que des fonctions mathématiques opérant sur ces tableaux.

  • matplotlib est une bibliothèque du langage de programmation Python destinée à tracer et visualiser des données sous forme de graphiques.

  • seaborn est une bibliothèque de visualisation Python basée sur matplotlib. Elle fournit une interface de haut niveau pour dessiner des graphiques statistiques attrayants.

  • keras est l'API de haut niveau de TensorFlow.

  • sklearn est une bibliothèque libre Python destinée à l'apprentissage automatique.

  • pickle est principalement utilisé pour sérialiser et désérialiser une structure objet Python. En d'autres termes, c'est le processus de conversion d'un objet Python en un flux d'octets pour le stocker dans un fichier/base de données, maintenir l'état du programme entre les sessions ou transporter des données sur le réseau.
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from tensorflow import keras
from keras import layers
import seaborn as sns
import pickle
from sklearn import svm
from sklearn.svm import SVR
from sklearn.metrics import accuracy_score, precision_score, recall_score, f1_score, confusion_matrix
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression

Etude exploratoire des données

Définition des colonnes

Dans le domaine de la science des données, la première chose à faire est de bien comprendre les données, ainsi et dans ce même sens, nous avons défini les colonnes comme suit :

  • CRIM: per capita crime rate by town.

  • ZN: proportion of residential land zoned for lots over 25,000 sq.ft.

  • INDUS: proportion of non-retail business acres per town.

  • CHAS: Charles River dummy variable (= 1 if tract bounds river; 0 otherwise).

  • NOX: nitric oxides concentration (parts per 10 million).

  • RM: average number of rooms per dwelling.

  • AGE: proportion of owner-occupied units built prior to 1940.

  • DIS: weighted distances to five Boston employment centres.

  • RAD: index of accessibility to radial highways.

  • TAX: full-value property-tax rate per $10,000.

  • PTRATIO: pupil-teacher ratio by town.

  • B: 1000(Bk - 0.63)^2 where Bk is the proportion of black people by town.

  • LSTAT: % lower status of the population.

  • MEDV: our Target, Median value of owner-occupied homes in $1000's

Feature engineering

# Importer le dataset
from sklearn.datasets import load_boston
boston = load_boston()

# Afficher les ééments clés du dataset
boston.keys()

Output

dict_keys(['data', 'target', 'feature_names', 'DESCR', 'filename', 'data_module'])

## Afficher la description du dataset
print(boston.DESCR)
Output

.. _boston_dataset:

Boston house prices dataset

Data Set Characteristics: 

:Number of Instances: 506

:Number of Attributes: 13 numeric/categorical predictive. Median Value (attribute 14) is usually the target.

:Attribute Information (in order):
    - CRIM     per capita crime rate by town
    - ZN       proportion of residential land zoned for lots over 25,000 sq.ft.
    - INDUS    proportion of non-retail business acres per town
    - CHAS     Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)
    - NOX      nitric oxides concentration (parts per 10 million)
    - RM       average number of rooms per dwelling
    - AGE      proportion of owner-occupied units built prior to 1940
    - DIS      weighted distances to five Boston employment centres
    - RAD      index of accessibility to radial highways
    - TAX      full-value property-tax rate per $10,000
    - PTRATIO  pupil-teacher ratio by town
    - B        1000(Bk - 0.63)^2 where Bk is the proportion of black people by town
    - LSTAT    % lower status of the population
    - MEDV     Median value of owner-occupied homes in $1000's

:Missing Attribute Values: None

:Creator: Harrison, D. and Rubinfeld, D.L.

This is a copy of UCI ML housing dataset. https://archive.ics.uci.edu/ml/machine-learning-databases/housing/

This dataset was taken from the StatLib library which is maintained at Carnegie Mellon University.

The Boston house-price data of Harrison, D. and Rubinfeld, D.L. 'Hedonic prices and the demand for clean air', J. Environ. Economics & Management, vol.5, 81-102, 1978. Used in Belsley, Kuh & Welsch, 'Regression diagnostics ...', Wiley, 1980. N.B. Various transformations are used in the table on pages 244-261 of the latter.

The Boston house-price data has been used in many machine learning papers that address regression problems.

.. topic:: References

  • Belsley, Kuh & Welsch, 'Regression diagnostics: Identifying Influential Data and Sources of Collinearity', Wiley, 1980. 244-261.
  • Quinlan,R. (1993). Combining Instance-Based and Model-Based Learning. In Proceedings on the Tenth International Conference of Machine Learning, 236-243, University of Massachusetts, Amherst. Morgan Kaufmann.
# Afficher le contenu des features 
print(boston.data)
Output

[[6.3200e-03 1.8000e+01 2.3100e+00 ... 1.5300e+01 3.9690e+02 4.9800e+00]

[2.7310e-02 0.e+00 7.0700e+00 ... 1.7800e+01 3.9690e+02 9.1400e+00]

[2.7290e-02 0.e+00 7.0700e+00 ... 1.7800e+01 3.9283e+02 4.0300e+00]

...

[6.0760e-02 0.e+00 1.1930e+01 ... 2.1000e+01 3.9690e+02 5.6400e+00]

[1.0959e-01 0.e+00 1.1930e+01 ... 2.1000e+01 3.9345e+02 6.4800e+00]

[4.7410e-02 0.e+00 1.1930e+01 ... 2.1000e+01 3.9690e+02 7.8800e+00]]

# Afficher le contenu du label
print(boston.target)
Output

[24. 21.6 34.7 33.4 36.2 28.7 22.9 27.1 16.5 18.9 15. 18.9 21.7 20.4 18.2 19.9 23.1 17.5 20.2 18.2 13.6 19.6 15.2 14.5 15.6 13.9 16.6 14.8 18.4 21. 12.7 14.5 13.2 13.1 13.5 18.9 20. 21. 24.7 30.8 34.9 26.6 25.3 24.7 21.2 19.3 20. 16.6 14.4 19.4 19.7 20.5 25. 23.4 18.9 35.4 24.7 31.6 23.3 19.6 18.7 16. 22.2 25. 33. 23.5 19.4 22. 17.4 20.9 24.2 21.7 22.8 23.4 24.1 21.4 20. 20.8 21.2 20.3 28. 23.9 24.8 22.9 23.9 26.6 22.5 22.2 23.6 28.7 22.6 22. 22.9 25. 20.6 28.4 21.4 38.7 43.8 33.2 27.5 26.5 18.6 19.3 20.1 19.5 19.5 20.4 19.8 19.4 21.7 22.8 18.8 18.7 18.5 18.3 21.2 19.2 20.4 19.3 22. 20.3 20.5 17.3 18.8 21.4 15.7 16.2 18. 14.3 19.2 19.6 23. 18.4 15.6 18.1 17.4 17.1 13.3 17.8 14. 14.4 13.4 15.6 11.8 13.8 15.6 14.6 17.8 15.4 21.5 19.6 15.3 19.4 17. 15.6 13.1 41.3 24.3 23.3 27. 50. 50. 50. 22.7 25. 50. 23.8 23.8 22.3 17.4 19.1 23.1 23.6 22.6 29.4 23.2 24.6 29.9 37.2 39.8 36.2 37.9 32.5 26.4 29.6 50. 32. 29.8 34.9 37. 30.5 36.4 31.1 29.1 50. 33.3 30.3 34.6 34.9 32.9 24.1 42.3 48.5 50. 22.6 24.4 22.5 24.4 20. 21.7 19.3 22.4 28.1 23.7 25. 23.3 28.7 21.5 23. 26.7 21.7 27.5 30.1 44.8 50. 37.6 31.6 46.7 31.5 24.3 31.7 41.7 48.3 29. 24. 25.1 31.5 23.7 23.3 22. 20.1 22.2 23.7 17.6 18.5 24.3 20.5 24.5 26.2 24.4 24.8 29.6 42.8 21.9 20.9 44. 50. 36. 30.1 33.8 43.1 48.8 31. 36.5 22.8 30.7 50. 43.5 20.7 21.1 25.2 24.4 35.2 32.4 32. 33.2 33.1 29.1 35.1 45.4 35.4 46. 50. 32.2 22. 20.1 23.2 22.3 24.8 28.5 37.3 27.9 23.9 21.7 28.6 27.1 20.3 22.5 29. 24.8 22. 26.4 33.1 36.1 28.4 33.4 28.2 22.8 20.3 16.1 22.1 19.4 21.6 23.8 16.2 17.8 19.8 23.1 21. 23.8 23.1 20.4 18.5 25. 24.6 23. 22.2 19.3 22.6 19.8 17.1 19.4 22.2 20.7 21.1 19.5 18.5 20.6 19. 18.7 32.7 16.5 23.9 31.2 17.5 17.2 23.1 24.5 26.6 22.9 24.1 18.6 30.1 18.2 20.6 17.8 21.7 22.7 22.6 25. 19.9 20.8 16.8 21.9 27.5 21.9 23.1 50. 50. 50. 50. 50. 13.8 13.8 15. 13.9 13.3 13.1 10.2 10.4 10.9 11.3 12.3 8.8 7.2 10.5 7.4 10.2 11.5 15.1 23.2 9.7 13.8 12.7 13.1 12.5 8.5 5. 6.3 5.6 7.2 12.1 8.3 8.5 5. 11.9 27.9 17.2 27.5 15. 17.2 17.9 16.3 7. 7.2 7.5 10.4 8.8 8.4 16.7 14.2 20.8 13.4 11.7 8.3 10.2 10.9 11. 9.5 14.5 14.1 16.1 14.3 11.7 13.4 9.6 8.7 8.4 12.8 10.5 17.1 18.4 15.4 10.8 11.8 14.9 12.6 14.1 13. 13.4 15.2 16.1 17.8 14.9 14.1 12.7 13.5 14.9 20. 16.4 17.7 19.5 20.2 21.4 19.9 19. 19.1 19.1 20.1 19.9 19.6 23.2 29.8 13.8 13.3 16.7 12. 14.6 21.4 23. 23.7 25. 21.8 20.6 21.2 19.1 20.6 15.2 7. 8.1 13.6 20.1 21.8 24.5 23.1 19.7 18.3 21.2 17.5 16.8 22.4 20.6 23.9 22. 11.9]

# Afficher les noms des features
print(boston.feature_names)
Output

['CRIM' 'ZN' 'INDUS' 'CHAS' 'NOX' 'RM' 'AGE' 'DIS' 'RAD' 'TAX' 'PTRATIO' 'B' 'LSTAT']

# Transformer le boston dataset en Data Frame
dataset = pd.DataFrame(boston.data,columns=boston.feature_names)

# Afficher les 5 premières lignes du dataset
dataset.head(5)

Output
CRIM ZN INDUS CHAS NOX RM AGE DIS RAD TAX PTRATIO B LSTAT
0 0.00632 18.0 2.31 0.0 0.538 6.575 65.2 4.0900 1.0 296.0 15.3 396.90 4.98
1 0.02731 0.0 7.07 0.0 0.469 6.421 78.9 4.9671 2.0 242.0 17.8 396.90 9.14
2 0.02729 0.0 7.07 0.0 0.469 7.185 61.1 4.9671 2.0 242.0 17.8 392.83 4.03
3 0.03237 0.0 2.18 0.0 0.458 6.998 45.8 6.0622 3.0 222.0 18.7 394.63 2.94
4 0.06905 0.0 2.18 0.0 0.458 7.147 54.2 6.0622 3.0 222.0 18.7 396.90 5.33 

# Ajouter le label au dataset et lui nommer "Price"
dataset['MEDV'] = boston.target

# Afficher quelques informations de la data
dataset.info()

Output

<class 'pandas.core.frame.DataFrame'>

RangeIndex: 506 entries, 0 to 505

Data columns (total 14 columns):

# Column Non-Null Count Dtype
0 CRIM 506 non-null float64
1 ZN 506 non-null float64
2 INDUS 506 non-null float64
3 CHAS 506 non-null float64
4 NOX 506 non-null float64
5 RM 506 non-null float64
6 AGE 506 non-null float64
7 DIS 506 non-null float64
8 RAD 506 non-null float64
9 TAX 506 non-null float64
10 PTRATIO 506 non-null float64
11 B 506 non-null float64
12 LSTAT 506 non-null float64
13 MEDV 506 non-null float64

dtypes: float64(14)

memory usage: 55.5 KB

  • Le Dataset contient 506 lignes et 14 colonnes.
  • toutes les colonnes sont de type float64.
# Afficher une description statistique de la dataset
dataset.describe()
Output
CRIM ZN INDUS CHAS NOX RM AGE DIS RAD TAX PTRATIO B LSTAT MEDV
count 506.00 506.00 506.00 506.00 506.00 506.00 506.00 506.00 506.00 506.00 506.00 506.00 506.00 506.00
mean 3.61 11.36 11.13 0.06 0.55 6.28 68.57 3.79 9.54 408.23 18.45 356.67 12.65 22.53
std 8.60 23.32 6.86 0.25 0.11 0.70 28.14 2.10 8.70 168.53 2.16 91.29 7.14 9.19
min 0.006 0.00 0.46 0.00 0.38 3.56 2.90 1.12 1.00 187.00 12.60 0.32 1.73 5.00
25% 0.08 0.00 5.19 0.00 0.44 5.88 45.02 2.10 4.00 279.00 17.40 375.37 6.95 17.02
50% 0.25 0.00 9.69 0.00 0.53 6.20 77.50 3.20 5.00 330.00 19.05 391.44 11.36 21.20
75% 3.67 12.50 18.10 0.00 0.62 6.62 94.07 5.18 24.00 666.00 20.20 396.22 16.95 25.00
max 88.97 100.00 27.74 1.00 0.87 8.78 100.00 12.12 24.00 711.00 22.00 396.90 37.97 50.00 
# Afficher les valeurs NaN
dataset.isnull().sum()
Output
Column Number of NaN
CRIM 0
ZN 0
INDUS 0
CHAS 0
NOX 0
RM 0
AGE 0
DIS 0
RAD 0
TAX 0
PTRATIO 0
B 0
LSTAT 0
MEDV 0

dtype: int64

Note

Nous notons que le dataset ne contient pas de valeurs NaN.

Vizualisation des données

Matrice de corrélation

La matrice de corrélation indique les valeurs de corrélation, qui mesurent le degré de relation linéaire entre chaque paire de variables. Les valeurs de corrélation peuvent être comprises entre -1 et +1. Si les deux variables ont tendance à augmenter et à diminuer en même temps, la valeur de corrélation est positive. Lorsqu'une variable augmente alors que l'autre diminue, la valeur de corrélation est négative.

# Afficher la matrice de corrélation
matriceCorr = data.corr().round(1)
sns.heatmap(data=matriceCorr, annot = True)
Output

Matrice de Corrélation

Note

Nous notons qu'il y a plusieurs correlations entre les colonnes, mais nous n'allons pas prendre en considération ces corrélations pour l'instant parce que les réseaux de neuronnes peuvent détecter les corrélations ainsi les traiter.

Représentations des colonnes deux à deux

# Afficher les représentations des colonnes deux à deux
sns.pairplot(dataset)
Output

Pair Plot

# Afficher "MEDV" en fonction de "CRIM"
plt.scatter(dataset['CRIM'],dataset['MEDV'])
plt.xlabel("Crime Rate")
plt.ylabel("Medv")
Output

Pair Plot

# Afficher "RM" en fonction de "MEDV"
plt.scatter(dataset['RM'],dataset['MEDV'])
plt.xlabel("RM")
plt.ylabel("Medv")
Output

Pair Plot

# Tracer les données et l'ajustement d'un modèle de régression linéaire MEDV=f(RM)
sns.regplot(x="RM",y="MEDV",data=dataset)
Output

Pair Plot

# Tracer les données et l'ajustement d'un modèle de régression linéaire MEDV=f(LSTAT)
sns.regplot(x="LSTAT",y="MEDV",data=dataset)
Output

Pair Plot

# Tracer les données et l'ajustement d'un modèle de régression linéaire MEDV=f(CHAS)
sns.regplot(x="CHAS",y="MEDV",data=dataset)
Output

Pair Plot

# Tracer les données et l'ajustement d'un modèle de régression linéaire MEDV=f(PTRATIO)
sns.regplot(x="PTRATIO",y="MEDV",data=dataset)
Output

Pair Plot

Implémentation des modèles

Préparation des des vecteurs d'entrainement

Maintenant nous allons implémenter et entrainer plusieurs modèles de machine learning afin de choisir le meilleur, mais avant nous devons définir les features, le target et décomposer le dataset en data d'entrainement et data du test. 

# Définir les features
X = dataset.drop('MEDV', axis=1)

# Définir le target
y = dataset['MEDV']

# Décomposer la data en 80% pour l'entrainement et 20% pour le test
X_train, X_test, y_train, y_test = train_test_split(X,y,test_size=0.2,random_state=42)

# Afficher la taille de X_train, X_test, y_train, y_test
print("la taille de X_train est :", X_train.shape)
print("la taille de X_test est :", X_test.shape)
print("la taille de y_train est :", y_train.shape)
print("la taille de y_test est :", y_test.shape)

Output

la taille de X_train est : (404, 13)

la taille de X_test est : (102, 13)

la taille de y_train est : (404,)

la taille de y_test est : (102,)

# Norrmalisation des données en utilisant le StandardScaler (x-mean)/(std)
from sklearn.preprocessing import StandardScaler
scaler = StandardScaler()
X_train = scaler.fit_transform(X_train)
X_test = scaler.transform(X_test)

Réseaux de neurones denses DNN

num_layer1 = 50
num_layer2 = 50

model = keras.models.Sequential(name='DNN')
model.add(layers.Input((13,), name="Couche_in"))
model.add(layers.Dense(num_layer1, activation='relu', name='Couche_cachee1'))
model.add(layers.Dense(num_layer2, activation='relu', name='Couche_cachee2'))
model.add(layers.Dense(1, name='Couche_out'))

model.compile(optimizer='adam',
              loss='mse',
              metrics=['mae'])

model.summary()

Output

Model: "DNN"

Layer (type) Output Shape Param #
Couche_cachee1 (Dense) (None, 50) 700
Couche_cachee2 (Dense) (None, 50) 2550
Couche_out (Dense) (None, 1) 51

Total params: 3,301

Trainable params: 3,301

Non-trainable params: 0

# Lancer l'entrainement du modèle
hist = model.fit(X_train,
                 y_train,
                 epochs=400,
                 batch_size=50)
Output

Epoch 1/400 9/9 [==============================] - 1s 4ms/step - loss: 557.3136 - mae: 21.6968

Epoch 2/400 9/9 [==============================] - 0s 3ms/step - loss: 520.2143 - mae: 20.8262

Epoch 3/400 9/9 [==============================] - 0s 3ms/step - loss: 475.9985 - mae: 19.7651

Epoch 4/400 9/9 [==============================] - 0s 3ms/step - loss: 423.2747 - mae: 18.4109

Epoch 5/400 9/9 [==============================] - 0s 3ms/step - loss: 361.1457 - mae: 16.7136

Epoch 6/400 9/9 [==============================] - 0s 3ms/step - loss: 289.6600 - mae: 14.6173

Epoch 7/400 9/9 [==============================] - 0s 3ms/step - loss: 219.4651 - mae: 12.2325

Epoch 8/400 9/9 [==============================] - 0s 3ms/step - loss: 158.8683 - mae: 10.0692

Epoch 9/400 9/9 [==============================] - 0s 3ms/step - loss: 116.7818 - mae: 8.3857

Epoch 10/400 9/9 [==============================] - 0s 3ms/step - loss: 91.9504 - mae: 7.3596

Epoch 11/400 9/9 [==============================] - 0s 3ms/step - loss: 76.5844 - mae: 6.6405

Epoch 12/400 9/9 [==============================] - 0s 8ms/step - loss: 62.4096 - mae: 5.9445

Epoch 13/400 9/9 [==============================] - 0s 3ms/step - loss: 49.9997 - mae: 5.3151

Epoch 14/400 9/9 [==============================] - 0s 3ms/step - loss: 40.8705 - mae: 4.8252

Epoch 15/400 9/9 [==============================] - 0s 3ms/step - loss: 34.1865 - mae: 4.4059

Epoch 16/400 9/9 [==============================] - 0s 3ms/step - loss: 29.6209 - mae: 4.0728

Epoch 17/400 9/9 [==============================] - 0s 3ms/step - loss: 26.3418 - mae: 3.8037

Epoch 18/400 9/9 [==============================] - 0s 3ms/step - loss: 24.0514 - mae: 3.6174

Epoch 19/400 9/9 [==============================] - 0s 3ms/step - loss: 22.3640 - mae: 3.4849

Epoch 20/400 9/9 [==============================] - 0s 3ms/step - loss: 21.0404 - mae: 3.3751

Epoch 21/400 9/9 [==============================] - 0s 3ms/step - loss: 20.0787 - mae: 3.2945

Epoch 22/400 9/9 [==============================] - 0s 4ms/step - loss: 19.1893 - mae: 3.2271

Epoch 23/400 9/9 [==============================] - 0s 3ms/step - loss: 18.4744 - mae: 3.1858

Epoch 24/400 9/9 [==============================] - 0s 3ms/step - loss: 17.9731 - mae: 3.1562

Epoch 25/400 9/9 [==============================] - 0s 3ms/step - loss: 17.4404 - mae: 3.0923

Epoch 26/400 9/9 [==============================] - 0s 3ms/step - loss: 16.9731 - mae: 3.0298

Epoch 27/400 9/9 [==============================] - 0s 3ms/step - loss: 16.6027 - mae: 2.9926

Epoch 28/400 9/9 [==============================] - 0s 3ms/step - loss: 16.2943 - mae: 2.9884

Epoch 29/400 9/9 [==============================] - 0s 3ms/step - loss: 16.1183 - mae: 2.9904

Epoch 30/400 9/9 [==============================] - 0s 3ms/step - loss: 15.8298 - mae: 2.9535

Epoch 31/400 9/9 [==============================] - 0s 3ms/step - loss: 15.4369 - mae: 2.8914

Epoch 32/400 9/9 [==============================] - 0s 3ms/step - loss: 15.2457 - mae: 2.8531

Epoch 33/400 9/9 [==============================] - 0s 3ms/step - loss: 15.0859 - mae: 2.8292

Epoch 34/400 9/9 [==============================] - 0s 3ms/step - loss: 14.8123 - mae: 2.8021

Epoch 35/400 9/9 [==============================] - 0s 2ms/step - loss: 14.7016 - mae: 2.8349

Epoch 36/400 9/9 [==============================] - 0s 3ms/step - loss: 14.7392 - mae: 2.8583

Epoch 37/400 9/9 [==============================] - 0s 3ms/step - loss: 14.4040 - mae: 2.7936

Epoch 38/400 9/9 [==============================] - 0s 3ms/step - loss: 14.1673 - mae: 2.7549

Epoch 39/400 9/9 [==============================] - 0s 3ms/step - loss: 14.0135 - mae: 2.7394

Epoch 40/400 9/9 [==============================] - 0s 3ms/step - loss: 13.7766 - mae: 2.7193

Epoch 41/400 9/9 [==============================] - 0s 3ms/step - loss: 13.6497 - mae: 2.7049

Epoch 42/400 9/9 [==============================] - 0s 3ms/step - loss: 13.8148 - mae: 2.7279

Epoch 43/400 9/9 [==============================] - 0s 3ms/step - loss: 13.5806 - mae: 2.7368

Epoch 44/400 9/9 [==============================] - 0s 4ms/step - loss: 13.3692 - mae: 2.6903

Epoch 45/400 9/9 [==============================] - 0s 3ms/step - loss: 13.1967 - mae: 2.6587

Epoch 46/400 9/9 [==============================] - 0s 3ms/step - loss: 13.0199 - mae: 2.6454

Epoch 47/400 9/9 [==============================] - 0s 3ms/step - loss: 13.0109 - mae: 2.6521

Epoch 48/400 9/9 [==============================] - 0s 3ms/step - loss: 12.9398 - mae: 2.6408

Epoch 49/400 9/9 [==============================] - 0s 3ms/step - loss: 12.8580 - mae: 2.6236

Epoch 50/400 9/9 [==============================] - 0s 3ms/step - loss: 12.8581 - mae: 2.6218

Epoch 51/400 9/9 [==============================] - 0s 3ms/step - loss: 12.7277 - mae: 2.6095

Epoch 52/400 9/9 [==============================] - 0s 3ms/step - loss: 12.5262 - mae: 2.5825

Epoch 53/400 9/9 [==============================] - 0s 3ms/step - loss: 12.5404 - mae: 2.5921

Epoch 54/400 9/9 [==============================] - 0s 3ms/step - loss: 12.3580 - mae: 2.5644

Epoch 55/400 9/9 [==============================] - 0s 3ms/step - loss: 12.2630 - mae: 2.5534

Epoch 56/400 9/9 [==============================] - 0s 3ms/step - loss: 12.1893 - mae: 2.5394

Epoch 57/400 9/9 [==============================] - 0s 4ms/step - loss: 12.0945 - mae: 2.5230

Epoch 58/400 9/9 [==============================] - 0s 3ms/step - loss: 12.1561 - mae: 2.5299

Epoch 59/400 9/9 [==============================] - 0s 3ms/step - loss: 12.0405 - mae: 2.5175

Epoch 60/400 9/9 [==============================] - 0s 3ms/step - loss: 12.0079 - mae: 2.4976

Epoch 61/400 9/9 [==============================] - 0s 3ms/step - loss: 11.8621 - mae: 2.4903

Epoch 62/400 9/9 [==============================] - 0s 3ms/step - loss: 11.7536 - mae: 2.4790

Epoch 63/400 9/9 [==============================] - 0s 3ms/step - loss: 11.8308 - mae: 2.4806

Epoch 64/400 9/9 [==============================] - 0s 3ms/step - loss: 11.8091 - mae: 2.4820

Epoch 65/400 9/9 [==============================] - 0s 3ms/step - loss: 11.6384 - mae: 2.4957

Epoch 66/400 9/9 [==============================] - 0s 3ms/step - loss: 11.8385 - mae: 2.5424

Epoch 67/400 9/9 [==============================] - 0s 4ms/step - loss: 11.7600 - mae: 2.5212

Epoch 68/400 9/9 [==============================] - 0s 3ms/step - loss: 11.4665 - mae: 2.4539

Epoch 69/400 9/9 [==============================] - 0s 3ms/step - loss: 11.4085 - mae: 2.4327

Epoch 70/400 9/9 [==============================] - 0s 3ms/step - loss: 11.3790 - mae: 2.4286

Epoch 71/400 9/9 [==============================] - 0s 4ms/step - loss: 11.2816 - mae: 2.4209

Epoch 72/400 9/9 [==============================] - 0s 4ms/step - loss: 11.2071 - mae: 2.4173

Epoch 73/400 9/9 [==============================] - 0s 3ms/step - loss: 11.1422 - mae: 2.4088

Epoch 74/400 9/9 [==============================] - 0s 3ms/step - loss: 11.0773 - mae: 2.4023

Epoch 75/400 9/9 [==============================] - 0s 3ms/step - loss: 11.0161 - mae: 2.3964

Epoch 76/400 9/9 [==============================] - 0s 4ms/step - loss: 11.0054 - mae: 2.3888

Epoch 77/400 9/9 [==============================] - 0s 3ms/step - loss: 10.8978 - mae: 2.3807

Epoch 78/400 9/9 [==============================] - 0s 3ms/step - loss: 10.8926 - mae: 2.3930

Epoch 79/400 9/9 [==============================] - 0s 3ms/step - loss: 10.9182 - mae: 2.3996

Epoch 80/400 9/9 [==============================] - 0s 3ms/step - loss: 10.9850 - mae: 2.4115

Epoch 81/400 9/9 [==============================] - 0s 3ms/step - loss: 11.0064 - mae: 2.3867

Epoch 82/400 9/9 [==============================] - 0s 3ms/step - loss: 11.1898 - mae: 2.3889

Epoch 83/400 9/9 [==============================] - 0s 3ms/step - loss: 10.7470 - mae: 2.3746

Epoch 84/400 9/9 [==============================] - 0s 3ms/step - loss: 10.8092 - mae: 2.4083

Epoch 85/400 9/9 [==============================] - 0s 3ms/step - loss: 10.5877 - mae: 2.3942

Epoch 86/400 9/9 [==============================] - 0s 4ms/step - loss: 10.5039 - mae: 2.3632

Epoch 87/400 9/9 [==============================] - 0s 3ms/step - loss: 10.5263 - mae: 2.3636

Epoch 88/400 9/9 [==============================] - 0s 3ms/step - loss: 10.4007 - mae: 2.3452

Epoch 89/400 9/9 [==============================] - 0s 3ms/step - loss: 10.3052 - mae: 2.3390

Epoch 90/400 9/9 [==============================] - 0s 3ms/step - loss: 10.2830 - mae: 2.3430

Epoch 91/400 9/9 [==============================] - 0s 3ms/step - loss: 10.2626 - mae: 2.3305

Epoch 92/400 9/9 [==============================] - 0s 3ms/step - loss: 10.2998 - mae: 2.3301

Epoch 93/400 9/9 [==============================] - 0s 3ms/step - loss: 10.3857 - mae: 2.3660

Epoch 94/400 9/9 [==============================] - 0s 3ms/step - loss: 10.2242 - mae: 2.3430

Epoch 95/400 9/9 [==============================] - 0s 3ms/step - loss: 10.0685 - mae: 2.3185

Epoch 96/400 9/9 [==============================] - 0s 3ms/step - loss: 10.0650 - mae: 2.3192

Epoch 97/400 9/9 [==============================] - 0s 3ms/step - loss: 10.0117 - mae: 2.3269

Epoch 98/400 9/9 [==============================] - 0s 3ms/step - loss: 10.0123 - mae: 2.3178

Epoch 99/400 9/9 [==============================] - 0s 3ms/step - loss: 9.9383 - mae: 2.3025

Epoch 100/400 9/9 [==============================] - 0s 4ms/step - loss: 9.8653 - mae: 2.2933

Epoch 101/400 9/9 [==============================] - 0s 3ms/step - loss: 9.9191 - mae: 2.3033

Epoch 102/400 9/9 [==============================] - 0s 3ms/step - loss: 9.8622 - mae: 2.2823

Epoch 103/400 9/9 [==============================] - 0s 3ms/step - loss: 9.7497 - mae: 2.2569

Epoch 104/400 9/9 [==============================] - 0s 3ms/step - loss: 9.6942 - mae: 2.2639

Epoch 105/400 9/9 [==============================] - 0s 4ms/step - loss: 9.6776 - mae: 2.2588

Epoch 106/400 9/9 [==============================] - 0s 3ms/step - loss: 9.7455 - mae: 2.2674

Epoch 107/400 9/9 [==============================] - 0s 3ms/step - loss: 9.5815 - mae: 2.2458

Epoch 108/400 9/9 [==============================] - 0s 3ms/step - loss: 9.5837 - mae: 2.2518

Epoch 109/400 9/9 [==============================] - 0s 3ms/step - loss: 9.4691 - mae: 2.2334

Epoch 110/400 9/9 [==============================] - 0s 3ms/step - loss: 9.4230 - mae: 2.2271

Epoch 111/400 9/9 [==============================] - 0s 3ms/step - loss: 9.4083 - mae: 2.2276

Epoch 112/400 9/9 [==============================] - 0s 3ms/step - loss: 9.3655 - mae: 2.2257

Epoch 113/400 9/9 [==============================] - 0s 3ms/step - loss: 9.3588 - mae: 2.2105

Epoch 114/400 9/9 [==============================] - 0s 3ms/step - loss: 9.6419 - mae: 2.2598

Epoch 115/400 9/9 [==============================] - 0s 3ms/step - loss: 9.5963 - mae: 2.2624

Epoch 116/400 9/9 [==============================] - 0s 3ms/step - loss: 9.4118 - mae: 2.2251

Epoch 117/400 9/9 [==============================] - 0s 3ms/step - loss: 9.2462 - mae: 2.2159

Epoch 118/400 9/9 [==============================] - 0s 3ms/step - loss: 9.2559 - mae: 2.2230

Epoch 119/400 9/9 [==============================] - 0s 3ms/step - loss: 9.1834 - mae: 2.2073

Epoch 120/400 9/9 [==============================] - 0s 3ms/step - loss: 9.1216 - mae: 2.1961

Epoch 121/400 9/9 [==============================] - 0s 4ms/step - loss: 9.1227 - mae: 2.1902

Epoch 122/400 9/9 [==============================] - 0s 3ms/step - loss: 9.1087 - mae: 2.1876

Epoch 123/400 9/9 [==============================] - 0s 4ms/step - loss: 9.1089 - mae: 2.1849

Epoch 124/400 9/9 [==============================] - 0s 3ms/step - loss: 9.0926 - mae: 2.1861

Epoch 125/400 9/9 [==============================] - 0s 3ms/step - loss: 9.2096 - mae: 2.2124

Epoch 126/400 9/9 [==============================] - 0s 4ms/step - loss: 9.0495 - mae: 2.1710

Epoch 127/400 9/9 [==============================] - 0s 3ms/step - loss: 8.9340 - mae: 2.1624

Epoch 128/400 9/9 [==============================] - 0s 4ms/step - loss: 8.8782 - mae: 2.1619

Epoch 129/400 9/9 [==============================] - 0s 3ms/step - loss: 8.8453 - mae: 2.1571

Epoch 130/400 9/9 [==============================] - 0s 4ms/step - loss: 8.9253 - mae: 2.1674

Epoch 131/400 9/9 [==============================] - 0s 5ms/step - loss: 8.8694 - mae: 2.1647

Epoch 132/400 9/9 [==============================] - 0s 4ms/step - loss: 8.7110 - mae: 2.1455

Epoch 133/400 9/9 [==============================] - 0s 4ms/step - loss: 8.7117 - mae: 2.1463

Epoch 134/400 9/9 [==============================] - 0s 3ms/step - loss: 8.7079 - mae: 2.1490

Epoch 135/400 9/9 [==============================] - 0s 4ms/step - loss: 8.6802 - mae: 2.1438

Epoch 136/400 9/9 [==============================] - 0s 3ms/step - loss: 8.6549 - mae: 2.1312

Epoch 137/400 9/9 [==============================] - 0s 3ms/step - loss: 8.5795 - mae: 2.1202

Epoch 138/400 9/9 [==============================] - 0s 3ms/step - loss: 8.5459 - mae: 2.1143

Epoch 139/400 9/9 [==============================] - 0s 3ms/step - loss: 8.5602 - mae: 2.1233

Epoch 140/400 9/9 [==============================] - 0s 3ms/step - loss: 8.4806 - mae: 2.1126

Epoch 141/400 9/9 [==============================] - 0s 3ms/step - loss: 8.4711 - mae: 2.1127

Epoch 142/400 9/9 [==============================] - 0s 3ms/step - loss: 8.4310 - mae: 2.1130

Epoch 143/400 9/9 [==============================] - 0s 3ms/step - loss: 8.3803 - mae: 2.1100

Epoch 144/400 9/9 [==============================] - 0s 3ms/step - loss: 8.4019 - mae: 2.1182

Epoch 145/400 9/9 [==============================] - 0s 3ms/step - loss: 8.5072 - mae: 2.1415

Epoch 146/400 9/9 [==============================] - 0s 3ms/step - loss: 8.4077 - mae: 2.1234

Epoch 147/400 9/9 [==============================] - 0s 3ms/step - loss: 8.3219 - mae: 2.1120

Epoch 148/400 9/9 [==============================] - 0s 3ms/step - loss: 8.2850 - mae: 2.1045

Epoch 149/400 9/9 [==============================] - 0s 3ms/step - loss: 8.2003 - mae: 2.0864

Epoch 150/400 9/9 [==============================] - 0s 3ms/step - loss: 8.3044 - mae: 2.1012

Epoch 151/400 9/9 [==============================] - 0s 3ms/step - loss: 8.1278 - mae: 2.0764

Epoch 152/400 9/9 [==============================] - 0s 3ms/step - loss: 8.1840 - mae: 2.0984

Epoch 153/400 9/9 [==============================] - 0s 3ms/step - loss: 8.0466 - mae: 2.0698

Epoch 154/400 9/9 [==============================] - 0s 3ms/step - loss: 8.0476 - mae: 2.0702

Epoch 155/400 9/9 [==============================] - 0s 3ms/step - loss: 8.0402 - mae: 2.0748

Epoch 156/400 9/9 [==============================] - 0s 3ms/step - loss: 7.9566 - mae: 2.0641

Epoch 157/400 9/9 [==============================] - 0s 3ms/step - loss: 7.9516 - mae: 2.0667

Epoch 158/400 9/9 [==============================] - 0s 3ms/step - loss: 7.9795 - mae: 2.0733

Epoch 159/400 9/9 [==============================] - 0s 4ms/step - loss: 7.8663 - mae: 2.0591

Epoch 160/400 9/9 [==============================] - 0s 3ms/step - loss: 7.8300 - mae: 2.0529

Epoch 161/400 9/9 [==============================] - 0s 3ms/step - loss: 7.8782 - mae: 2.0532

Epoch 162/400 9/9 [==============================] - 0s 3ms/step - loss: 7.7560 - mae: 2.0371

Epoch 163/400 9/9 [==============================] - 0s 3ms/step - loss: 7.9327 - mae: 2.0501

Epoch 164/400 9/9 [==============================] - 0s 3ms/step - loss: 8.0039 - mae: 2.0472

Epoch 165/400 9/9 [==============================] - 0s 4ms/step - loss: 7.8326 - mae: 2.0383

Epoch 166/400 9/9 [==============================] - 0s 3ms/step - loss: 7.7433 - mae: 2.0366

Epoch 167/400 9/9 [==============================] - 0s 3ms/step - loss: 7.7063 - mae: 2.0403

Epoch 168/400 9/9 [==============================] - 0s 4ms/step - loss: 7.6165 - mae: 2.0247

Epoch 169/400 9/9 [==============================] - 0s 3ms/step - loss: 7.6203 - mae: 2.0237

Epoch 170/400 9/9 [==============================] - 0s 4ms/step - loss: 7.7583 - mae: 2.0332

Epoch 171/400 9/9 [==============================] - 0s 4ms/step - loss: 7.7060 - mae: 2.0474

Epoch 172/400 9/9 [==============================] - 0s 4ms/step - loss: 7.7214 - mae: 2.0453

Epoch 173/400 9/9 [==============================] - 0s 4ms/step - loss: 7.5782 - mae: 2.0151

Epoch 174/400 9/9 [==============================] - 0s 3ms/step - loss: 7.4870 - mae: 1.9941

Epoch 175/400 9/9 [==============================] - 0s 3ms/step - loss: 7.4292 - mae: 1.9942

Epoch 176/400 9/9 [==============================] - 0s 3ms/step - loss: 7.4034 - mae: 1.9908

Epoch 177/400 9/9 [==============================] - 0s 3ms/step - loss: 7.3374 - mae: 1.9794

Epoch 178/400 9/9 [==============================] - 0s 3ms/step - loss: 7.3651 - mae: 1.9837

Epoch 179/400 9/9 [==============================] - 0s 3ms/step - loss: 7.3334 - mae: 1.9801

Epoch 180/400 9/9 [==============================] - 0s 3ms/step - loss: 7.2986 - mae: 1.9715

Epoch 181/400 9/9 [==============================] - 0s 3ms/step - loss: 7.3080 - mae: 1.9842

Epoch 182/400 9/9 [==============================] - 0s 3ms/step - loss: 7.2384 - mae: 1.9710

Epoch 183/400 9/9 [==============================] - 0s 3ms/step - loss: 7.2382 - mae: 1.9695

Epoch 184/400 9/9 [==============================] - 0s 4ms/step - loss: 7.1499 - mae: 1.9672

Epoch 185/400 9/9 [==============================] - 0s 4ms/step - loss: 7.2522 - mae: 1.9746

Epoch 186/400 9/9 [==============================] - 0s 3ms/step - loss: 7.1246 - mae: 1.9721

Epoch 187/400 9/9 [==============================] - 0s 3ms/step - loss: 7.0991 - mae: 1.9624

Epoch 188/400 9/9 [==============================] - 0s 4ms/step - loss: 7.0756 - mae: 1.9483

Epoch 189/400 9/9 [==============================] - 0s 3ms/step - loss: 7.1697 - mae: 1.9584

Epoch 190/400 9/9 [==============================] - 0s 4ms/step - loss: 6.9426 - mae: 1.9408

Epoch 191/400 9/9 [==============================] - 0s 3ms/step - loss: 7.0492 - mae: 1.9498

Epoch 192/400 9/9 [==============================] - 0s 3ms/step - loss: 6.9617 - mae: 1.9392

Epoch 193/400 9/9 [==============================] - 0s 3ms/step - loss: 6.9713 - mae: 1.9391

Epoch 194/400 9/9 [==============================] - 0s 3ms/step - loss: 6.9681 - mae: 1.9466

Epoch 195/400 9/9 [==============================] - 0s 3ms/step - loss: 7.0815 - mae: 1.9378

Epoch 196/400 9/9 [==============================] - 0s 3ms/step - loss: 6.9769 - mae: 1.9339

Epoch 197/400 9/9 [==============================] - 0s 4ms/step - loss: 6.8727 - mae: 1.9210

Epoch 198/400 9/9 [==============================] - 0s 3ms/step - loss: 6.8014 - mae: 1.9227

Epoch 199/400 9/9 [==============================] - 0s 3ms/step - loss: 6.7703 - mae: 1.9244

Epoch 200/400 9/9 [==============================] - 0s 3ms/step - loss: 6.8127 - mae: 1.9195

Epoch 201/400 9/9 [==============================] - 0s 3ms/step - loss: 6.7469 - mae: 1.9105

Epoch 202/400 9/9 [==============================] - 0s 3ms/step - loss: 6.7515 - mae: 1.9144

Epoch 203/400 9/9 [==============================] - 0s 3ms/step - loss: 6.6946 - mae: 1.9044

Epoch 204/400 9/9 [==============================] - 0s 4ms/step - loss: 6.6362 - mae: 1.8985

Epoch 205/400 9/9 [==============================] - 0s 4ms/step - loss: 6.6175 - mae: 1.8955

Epoch 206/400 9/9 [==============================] - 0s 3ms/step - loss: 6.5702 - mae: 1.8874

Epoch 207/400 9/9 [==============================] - 0s 3ms/step - loss: 6.5716 - mae: 1.8900

Epoch 208/400 9/9 [==============================] - 0s 4ms/step - loss: 6.5384 - mae: 1.8846

Epoch 209/400 9/9 [==============================] - 0s 3ms/step - loss: 6.5449 - mae: 1.8830

Epoch 210/400 9/9 [==============================] - 0s 3ms/step - loss: 6.5513 - mae: 1.8749

Epoch 211/400 9/9 [==============================] - 0s 4ms/step - loss: 6.4929 - mae: 1.8735

Epoch 212/400 9/9 [==============================] - 0s 3ms/step - loss: 6.5068 - mae: 1.8747

Epoch 213/400 9/9 [==============================] - 0s 3ms/step - loss: 6.5305 - mae: 1.8740

Epoch 214/400 9/9 [==============================] - 0s 6ms/step - loss: 6.5346 - mae: 1.8997

Epoch 215/400 9/9 [==============================] - 0s 5ms/step - loss: 6.4906 - mae: 1.8849

Epoch 216/400 9/9 [==============================] - 0s 4ms/step - loss: 6.4162 - mae: 1.8608

Epoch 217/400 9/9 [==============================] - 0s 3ms/step - loss: 6.3261 - mae: 1.8522

Epoch 218/400 9/9 [==============================] - 0s 3ms/step - loss: 6.2750 - mae: 1.8420

Epoch 219/400 9/9 [==============================] - 0s 3ms/step - loss: 6.2780 - mae: 1.8364

Epoch 220/400 9/9 [==============================] - 0s 2ms/step - loss: 6.2991 - mae: 1.8530

Epoch 221/400 9/9 [==============================] - 0s 2ms/step - loss: 6.2668 - mae: 1.8361

Epoch 222/400 9/9 [==============================] - 0s 2ms/step - loss: 6.2077 - mae: 1.8355

Epoch 223/400 9/9 [==============================] - 0s 3ms/step - loss: 6.1889 - mae: 1.8245

Epoch 224/400 9/9 [==============================] - 0s 2ms/step - loss: 6.2081 - mae: 1.8289

Epoch 225/400 9/9 [==============================] - 0s 2ms/step - loss: 6.1629 - mae: 1.8108

Epoch 226/400 9/9 [==============================] - 0s 2ms/step - loss: 6.1450 - mae: 1.8226

Epoch 227/400 9/9 [==============================] - 0s 2ms/step - loss: 6.1505 - mae: 1.8359

Epoch 228/400 9/9 [==============================] - 0s 2ms/step - loss: 6.1221 - mae: 1.8270

Epoch 229/400 9/9 [==============================] - 0s 3ms/step - loss: 6.1809 - mae: 1.8272

Epoch 230/400 9/9 [==============================] - 0s 3ms/step - loss: 6.0162 - mae: 1.8011

Epoch 231/400 9/9 [==============================] - 0s 3ms/step - loss: 6.1452 - mae: 1.8393

Epoch 232/400 9/9 [==============================] - 0s 3ms/step - loss: 6.0985 - mae: 1.8124

Epoch 233/400 9/9 [==============================] - 0s 2ms/step - loss: 6.4570 - mae: 1.8844

Epoch 234/400 9/9 [==============================] - 0s 1ms/step - loss: 6.2272 - mae: 1.8489

Epoch 235/400 9/9 [==============================] - 0s 2ms/step - loss: 6.0741 - mae: 1.8166

Epoch 236/400 9/9 [==============================] - 0s 4ms/step - loss: 6.0031 - mae: 1.8197

Epoch 237/400 9/9 [==============================] - 0s 2ms/step - loss: 5.9739 - mae: 1.8037

Epoch 238/400 9/9 [==============================] - 0s 2ms/step - loss: 6.0253 - mae: 1.8145

Epoch 239/400 9/9 [==============================] - 0s 2ms/step - loss: 5.9134 - mae: 1.7873

Epoch 240/400 9/9 [==============================] - 0s 4ms/step - loss: 5.8683 - mae: 1.7957

Epoch 241/400 9/9 [==============================] - 0s 2ms/step - loss: 5.8370 - mae: 1.7853

Epoch 242/400 9/9 [==============================] - 0s 2ms/step - loss: 5.6954 - mae: 1.7598

Epoch 243/400 9/9 [==============================] - 0s 3ms/step - loss: 5.7053 - mae: 1.7696

Epoch 244/400 9/9 [==============================] - 0s 2ms/step - loss: 5.6565 - mae: 1.7627

Epoch 245/400 9/9 [==============================] - 0s 2ms/step - loss: 5.7158 - mae: 1.7734

Epoch 246/400 9/9 [==============================] - 0s 3ms/step - loss: 5.6415 - mae: 1.7482

Epoch 247/400 9/9 [==============================] - 0s 2ms/step - loss: 5.6077 - mae: 1.7508

Epoch 248/400 9/9 [==============================] - 0s 2ms/step - loss: 5.7397 - mae: 1.7653

Epoch 249/400 9/9 [==============================] - 0s 3ms/step - loss: 5.6152 - mae: 1.7499

Epoch 250/400 9/9 [==============================] - 0s 2ms/step - loss: 5.6300 - mae: 1.7422

Epoch 251/400 9/9 [==============================] - 0s 3ms/step - loss: 5.5146 - mae: 1.7228

Epoch 252/400 9/9 [==============================] - 0s 2ms/step - loss: 5.5786 - mae: 1.7403

Epoch 253/400 9/9 [==============================] - 0s 4ms/step - loss: 5.5123 - mae: 1.7385

Epoch 254/400 9/9 [==============================] - 0s 3ms/step - loss: 5.4784 - mae: 1.7380

Epoch 255/400 9/9 [==============================] - 0s 2ms/step - loss: 5.5062 - mae: 1.7488

Epoch 256/400 9/9 [==============================] - 0s 2ms/step - loss: 5.5507 - mae: 1.7410

Epoch 257/400 9/9 [==============================] - 0s 3ms/step - loss: 5.4626 - mae: 1.7239

Epoch 258/400 9/9 [==============================] - 0s 2ms/step - loss: 5.4174 - mae: 1.7266

Epoch 259/400 9/9 [==============================] - 0s 2ms/step - loss: 5.4086 - mae: 1.7221

Epoch 260/400 9/9 [==============================] - 0s 2ms/step - loss: 5.4384 - mae: 1.7349

Epoch 261/400 9/9 [==============================] - 0s 2ms/step - loss: 5.3345 - mae: 1.7105

Epoch 262/400 9/9 [==============================] - 0s 2ms/step - loss: 5.4374 - mae: 1.7372

Epoch 263/400 9/9 [==============================] - 0s 2ms/step - loss: 5.3719 - mae: 1.7141

Epoch 264/400 9/9 [==============================] - 0s 3ms/step - loss: 5.3888 - mae: 1.7084

Epoch 265/400 9/9 [==============================] - 0s 2ms/step - loss: 5.3843 - mae: 1.7203

Epoch 266/400 9/9 [==============================] - 0s 3ms/step - loss: 5.2937 - mae: 1.6940

Epoch 267/400 9/9 [==============================] - 0s 3ms/step - loss: 5.4328 - mae: 1.7181

Epoch 268/400 9/9 [==============================] - 0s 3ms/step - loss: 5.4531 - mae: 1.7435

Epoch 269/400 9/9 [==============================] - 0s 3ms/step - loss: 5.3654 - mae: 1.7205

Epoch 270/400 9/9 [==============================] - 0s 3ms/step - loss: 5.2651 - mae: 1.6883

Epoch 271/400 9/9 [==============================] - 0s 3ms/step - loss: 5.2156 - mae: 1.6878

Epoch 272/400 9/9 [==============================] - 0s 3ms/step - loss: 5.1566 - mae: 1.6785

Epoch 273/400 9/9 [==============================] - 0s 2ms/step - loss: 5.1215 - mae: 1.6799

Epoch 274/400 9/9 [==============================] - 0s 2ms/step - loss: 5.2469 - mae: 1.7029

Epoch 275/400 9/9 [==============================] - 0s 2ms/step - loss: 5.2710 - mae: 1.7097

Epoch 276/400 9/9 [==============================] - 0s 3ms/step - loss: 5.2278 - mae: 1.7117

Epoch 277/400 9/9 [==============================] - 0s 3ms/step - loss: 5.2271 - mae: 1.6952

Epoch 278/400 9/9 [==============================] - 0s 4ms/step - loss: 5.2615 - mae: 1.6881

Epoch 279/400 9/9 [==============================] - 0s 3ms/step - loss: 5.0883 - mae: 1.6659

Epoch 280/400 9/9 [==============================] - 0s 3ms/step - loss: 5.0631 - mae: 1.6695

Epoch 281/400 9/9 [==============================] - 0s 2ms/step - loss: 5.0413 - mae: 1.6467

Epoch 282/400 9/9 [==============================] - 0s 2ms/step - loss: 5.0614 - mae: 1.6541

Epoch 283/400 9/9 [==============================] - 0s 3ms/step - loss: 5.2651 - mae: 1.6999

Epoch 284/400 9/9 [==============================] - 0s 3ms/step - loss: 5.0937 - mae: 1.6658

Epoch 285/400 9/9 [==============================] - 0s 3ms/step - loss: 4.9900 - mae: 1.6483

Epoch 286/400 9/9 [==============================] - 0s 3ms/step - loss: 4.9686 - mae: 1.6482

Epoch 287/400 9/9 [==============================] - 0s 2ms/step - loss: 4.9377 - mae: 1.6493

Epoch 288/400 9/9 [==============================] - 0s 3ms/step - loss: 4.9239 - mae: 1.6397

Epoch 289/400 9/9 [==============================] - 0s 4ms/step - loss: 5.0049 - mae: 1.6458

Epoch 290/400 9/9 [==============================] - 0s 3ms/step - loss: 5.0257 - mae: 1.6677

Epoch 291/400 9/9 [==============================] - 0s 3ms/step - loss: 4.9595 - mae: 1.6502

Epoch 292/400 9/9 [==============================] - 0s 3ms/step - loss: 4.8937 - mae: 1.6199

Epoch 293/400 9/9 [==============================] - 0s 3ms/step - loss: 4.8048 - mae: 1.6054

Epoch 294/400 9/9 [==============================] - 0s 3ms/step - loss: 4.8538 - mae: 1.6189

Epoch 295/400 9/9 [==============================] - 0s 3ms/step - loss: 4.8086 - mae: 1.6214

Epoch 296/400 9/9 [==============================] - 0s 3ms/step - loss: 4.9100 - mae: 1.6228

Epoch 297/400 9/9 [==============================] - 0s 4ms/step - loss: 4.7689 - mae: 1.6057

Epoch 298/400 9/9 [==============================] - 0s 3ms/step - loss: 4.7895 - mae: 1.6120

Epoch 299/400 9/9 [==============================] - 0s 3ms/step - loss: 4.7679 - mae: 1.6074

Epoch 300/400 9/9 [==============================] - 0s 3ms/step - loss: 4.9302 - mae: 1.6508

Epoch 301/400 9/9 [==============================] - 0s 4ms/step - loss: 4.8806 - mae: 1.6316

Epoch 302/400 9/9 [==============================] - 0s 4ms/step - loss: 4.7871 - mae: 1.6054

Epoch 303/400 9/9 [==============================] - 0s 4ms/step - loss: 4.7296 - mae: 1.6088

Epoch 304/400 9/9 [==============================] - 0s 3ms/step - loss: 4.8593 - mae: 1.6316

Epoch 305/400 9/9 [==============================] - 0s 3ms/step - loss: 4.8702 - mae: 1.6265

Epoch 306/400 9/9 [==============================] - 0s 4ms/step - loss: 4.9289 - mae: 1.6436

Epoch 307/400 9/9 [==============================] - 0s 3ms/step - loss: 4.8258 - mae: 1.6364

Epoch 308/400 9/9 [==============================] - 0s 3ms/step - loss: 4.7715 - mae: 1.6131

Epoch 309/400 9/9 [==============================] - 0s 3ms/step - loss: 4.7257 - mae: 1.5808

Epoch 310/400 9/9 [==============================] - 0s 3ms/step - loss: 4.9713 - mae: 1.6622

Epoch 311/400 9/9 [==============================] - 0s 3ms/step - loss: 4.7670 - mae: 1.6311

Epoch 312/400 9/9 [==============================] - 0s 3ms/step - loss: 4.7790 - mae: 1.6104

Epoch 313/400 9/9 [==============================] - 0s 3ms/step - loss: 4.6748 - mae: 1.6186

Epoch 314/400 9/9 [==============================] - 0s 3ms/step - loss: 4.7386 - mae: 1.6191

Epoch 315/400 9/9 [==============================] - 0s 3ms/step - loss: 4.5862 - mae: 1.5769

Epoch 316/400 9/9 [==============================] - 0s 3ms/step - loss: 4.6310 - mae: 1.5809

Epoch 317/400 9/9 [==============================] - 0s 3ms/step - loss: 4.8212 - mae: 1.6367

Epoch 318/400 9/9 [==============================] - 0s 3ms/step - loss: 4.4685 - mae: 1.5482

Epoch 319/400 9/9 [==============================] - 0s 3ms/step - loss: 4.6965 - mae: 1.5876

Epoch 320/400 9/9 [==============================] - 0s 3ms/step - loss: 4.7098 - mae: 1.5959

Epoch 321/400 9/9 [==============================] - 0s 3ms/step - loss: 4.8441 - mae: 1.6635

Epoch 322/400 9/9 [==============================] - 0s 3ms/step - loss: 4.5366 - mae: 1.5945

Epoch 323/400 9/9 [==============================] - 0s 3ms/step - loss: 4.7188 - mae: 1.5974

Epoch 324/400 9/9 [==============================] - 0s 3ms/step - loss: 4.5682 - mae: 1.5611

Epoch 325/400 9/9 [==============================] - 0s 3ms/step - loss: 4.5609 - mae: 1.5801

Epoch 326/400 9/9 [==============================] - 0s 3ms/step - loss: 4.5395 - mae: 1.5852

Epoch 327/400 9/9 [==============================] - 0s 3ms/step - loss: 4.4885 - mae: 1.5625

Epoch 328/400 9/9 [==============================] - 0s 3ms/step - loss: 4.3885 - mae: 1.5423

Epoch 329/400 9/9 [==============================] - 0s 4ms/step - loss: 4.5206 - mae: 1.5739

Epoch 330/400 9/9 [==============================] - 0s 7ms/step - loss: 4.4114 - mae: 1.5382

Epoch 331/400 9/9 [==============================] - 0s 3ms/step - loss: 4.3323 - mae: 1.5197

Epoch 332/400 9/9 [==============================] - 0s 3ms/step - loss: 4.3240 - mae: 1.5208

Epoch 333/400 9/9 [==============================] - 0s 3ms/step - loss: 4.4238 - mae: 1.5322

Epoch 334/400 9/9 [==============================] - 0s 3ms/step - loss: 4.3662 - mae: 1.5501

Epoch 335/400 9/9 [==============================] - 0s 3ms/step - loss: 4.3211 - mae: 1.5324

Epoch 336/400 9/9 [==============================] - 0s 3ms/step - loss: 4.2283 - mae: 1.5031

Epoch 337/400 9/9 [==============================] - 0s 4ms/step - loss: 4.2960 - mae: 1.5352

Epoch 338/400 9/9 [==============================] - 0s 3ms/step - loss: 4.2662 - mae: 1.5223

Epoch 339/400 9/9 [==============================] - 0s 3ms/step - loss: 4.3856 - mae: 1.5406

Epoch 340/400 9/9 [==============================] - 0s 3ms/step - loss: 4.3143 - mae: 1.5513

Epoch 341/400 9/9 [==============================] - 0s 3ms/step - loss: 4.3948 - mae: 1.5666

Epoch 342/400 9/9 [==============================] - 0s 3ms/step - loss: 4.3177 - mae: 1.5356

Epoch 343/400 9/9 [==============================] - 0s 3ms/step - loss: 4.2848 - mae: 1.5331

Epoch 344/400 9/9 [==============================] - 0s 3ms/step - loss: 4.2723 - mae: 1.5274

Epoch 345/400 9/9 [==============================] - 0s 3ms/step - loss: 4.2018 - mae: 1.5079

Epoch 346/400 9/9 [==============================] - 0s 3ms/step - loss: 4.2182 - mae: 1.5171

Epoch 347/400 9/9 [==============================] - 0s 3ms/step - loss: 4.2083 - mae: 1.5251

Epoch 348/400 9/9 [==============================] - 0s 3ms/step - loss: 4.2829 - mae: 1.5318

Epoch 349/400 9/9 [==============================] - 0s 3ms/step - loss: 4.1793 - mae: 1.4975

Epoch 350/400 9/9 [==============================] - 0s 3ms/step - loss: 4.1535 - mae: 1.5021

Epoch 351/400 9/9 [==============================] - 0s 3ms/step - loss: 4.1689 - mae: 1.4901

Epoch 352/400 9/9 [==============================] - 0s 3ms/step - loss: 4.1737 - mae: 1.5091

Epoch 353/400 9/9 [==============================] - 0s 3ms/step - loss: 4.2916 - mae: 1.5423

Epoch 354/400 9/9 [==============================] - 0s 3ms/step - loss: 4.2486 - mae: 1.5089

Epoch 355/400 9/9 [==============================] - 0s 3ms/step - loss: 4.5061 - mae: 1.5545

Epoch 356/400 9/9 [==============================] - 0s 4ms/step - loss: 4.1563 - mae: 1.5199

Epoch 357/400 9/9 [==============================] - 0s 3ms/step - loss: 4.1927 - mae: 1.5353

Epoch 358/400 9/9 [==============================] - 0s 3ms/step - loss: 4.0238 - mae: 1.4803

Epoch 359/400 9/9 [==============================] - 0s 3ms/step - loss: 4.2785 - mae: 1.5282

Epoch 360/400 9/9 [==============================] - 0s 3ms/step - loss: 4.1957 - mae: 1.5044

Epoch 361/400 9/9 [==============================] - 0s 3ms/step - loss: 4.0877 - mae: 1.5101

Epoch 362/400 9/9 [==============================] - 0s 3ms/step - loss: 3.9776 - mae: 1.4631

Epoch 363/400 9/9 [==============================] - 0s 3ms/step - loss: 3.9758 - mae: 1.4540

Epoch 364/400 9/9 [==============================] - 0s 3ms/step - loss: 3.9303 - mae: 1.4430

Epoch 365/400 9/9 [==============================] - 0s 3ms/step - loss: 3.9630 - mae: 1.4558

Epoch 366/400 9/9 [==============================] - 0s 3ms/step - loss: 3.8929 - mae: 1.4350

Epoch 367/400 9/9 [==============================] - 0s 3ms/step - loss: 3.9009 - mae: 1.4355

Epoch 368/400 9/9 [==============================] - 0s 3ms/step - loss: 3.9361 - mae: 1.4656

Epoch 369/400 9/9 [==============================] - 0s 3ms/step - loss: 3.9120 - mae: 1.4496

Epoch 370/400 9/9 [==============================] - 0s 3ms/step - loss: 3.8926 - mae: 1.4374

Epoch 371/400 9/9 [==============================] - 0s 3ms/step - loss: 3.8675 - mae: 1.4317

Epoch 372/400 9/9 [==============================] - 0s 4ms/step - loss: 3.8442 - mae: 1.4272

Epoch 373/400 9/9 [==============================] - 0s 3ms/step - loss: 3.8265 - mae: 1.4365

Epoch 374/400 9/9 [==============================] - 0s 3ms/step - loss: 3.7951 - mae: 1.4227

Epoch 375/400 9/9 [==============================] - 0s 3ms/step - loss: 3.8109 - mae: 1.4185

Epoch 376/400 9/9 [==============================] - 0s 4ms/step - loss: 3.8171 - mae: 1.4315

Epoch 377/400 9/9 [==============================] - 0s 3ms/step - loss: 3.8079 - mae: 1.4224

Epoch 378/400 9/9 [==============================] - 0s 3ms/step - loss: 3.9359 - mae: 1.4343

Epoch 379/400 9/9 [==============================] - 0s 3ms/step - loss: 3.9052 - mae: 1.4712

Epoch 380/400 9/9 [==============================] - 0s 3ms/step - loss: 3.9682 - mae: 1.4686

Epoch 381/400 9/9 [==============================] - 0s 4ms/step - loss: 3.8712 - mae: 1.4372

Epoch 382/400 9/9 [==============================] - 0s 10ms/step - loss: 3.7983 - mae: 1.4193

Epoch 383/400 9/9 [==============================] - 0s 16ms/step - loss: 3.7823 - mae: 1.4226

Epoch 384/400 9/9 [==============================] - 0s 5ms/step - loss: 3.7303 - mae: 1.4140

Epoch 385/400 9/9 [==============================] - 0s 4ms/step - loss: 3.7204 - mae: 1.4044

Epoch 386/400 9/9 [==============================] - 0s 3ms/step - loss: 3.7432 - mae: 1.4152

Epoch 387/400 9/9 [==============================] - 0s 3ms/step - loss: 3.7204 - mae: 1.4045

Epoch 388/400 9/9 [==============================] - 0s 3ms/step - loss: 3.7163 - mae: 1.3980

Epoch 389/400 9/9 [==============================] - 0s 3ms/step - loss: 3.6538 - mae: 1.3896

Epoch 390/400 9/9 [==============================] - 0s 3ms/step - loss: 3.6510 - mae: 1.3874

Epoch 391/400 9/9 [==============================] - 0s 3ms/step - loss: 3.9399 - mae: 1.4741

Epoch 392/400 9/9 [==============================] - 0s 3ms/step - loss: 3.8155 - mae: 1.4265

Epoch 393/400 9/9 [==============================] - 0s 3ms/step - loss: 3.6893 - mae: 1.3884

Epoch 394/400 9/9 [==============================] - 0s 3ms/step - loss: 3.6876 - mae: 1.4176

Epoch 395/400 9/9 [==============================] - 0s 3ms/step - loss: 3.6896 - mae: 1.3905

Epoch 396/400 9/9 [==============================] - 0s 3ms/step - loss: 3.6180 - mae: 1.3828

Epoch 397/400 9/9 [==============================] - 0s 3ms/step - loss: 3.5933 - mae: 1.3773

Epoch 398/400 9/9 [==============================] - 0s 3ms/step - loss: 3.5719 - mae: 1.3750

Epoch 399/400 9/9 [==============================] - 0s 3ms/step - loss: 3.5381 - mae: 1.3641

Epoch 400/400 9/9 [==============================] - 0s 3ms/step - loss: 3.6085 - mae: 1.3688

# Applique le modèle sur la data du test
pred_test = model.predict(X_test)
pred_test.shape

# Evaluation du modèle
result_test = model.evaluate(X_test, y_test, verbose=0)
print('MSE test', round(result_test[0],2))
print('MAE test', round(result_test[1],2))

Output

MSE test 10.72

MAE test 2.11

Support Vector Regression SVR

# Définir le modèle
model_SVR = svm.SVR()

# Lancer l’apprentissage
model_SVR.fit(X_train,y_train)

Régression Linéaire LR

# Définir le modèle
regression=LinearRegression()

# Lancer l’apprentissage
regression.fit(X_train,y_train)

# Afficher les coefficients 
print(regression.coef_)

Output

[-1.00213533 0.69626862 0.27806485 0.7187384 -2.0223194 3.14523956 -0.17604788 -3.0819076 2.25140666 -1.76701378 -2.03775151 1.12956831 -3.61165842]

# Afficher the intercept
print(regression.intercept_)
Output

23.023938223938224

# Sur quels paramètres le modèle a entrainné
regression.get_params()
Output

{'copy_X': True,

'fit_intercept': True,

'n_jobs': None,

'normalize': 'deprecated',

'positive': False}