Polynomial regression

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import numpy as np
import matplotlib.pyplot as plt
from keras.models import Sequential
from keras.layers import Dense
from keras.optimizers import Adam

np.random.seed(0)
"""
data collection & preprocessing
"""
# number of points
points = 500
# input data
X = np.linspace(-3, 3, points)
# signal
# y = np.sin(X)
# signal + noise
# Adding noise on the sin signal to produce difficult data to the model to learn 
y = np.sin(X) + np.random.uniform(-0.5, 0.5, points)

# print(X)
# print(np.sin(X))
# print(np.random.uniform(-0.5, 0.5, points))
# print(y)
# plt.scatter(X, y)

"""
create model FFN
"""
model = Sequential()
# 1st hidden layer 50 nodes | 1 single input : price(size) : linear regrssion
model.add(Dense(50, activation='sigmoid', input_dim=1))
# 2nd hidden layer 30 nodes | activation layer : sigmoid : simple linear model 
model.add(Dense(30, activation='sigmoid'))
# output layer
model.add(Dense(1))

# error optimizer : gradient descent Adam
adam = Adam(lr=0.01)
# mean square error = Moyenne Quadratique  (fonction de coût)
model.compile(loss='mse', optimizer=adam)

"""
train

"""
model.fit(X, y, epochs=50)

"""
predictions of estimated values
"""
predictions = model.predict(X)

"""print prediction
"""
plt.scatter(X, y)
plt.plot(X, predictions, 'ro')
plt.show()

import numpy as np import matplotlib.pyplot as plt from keras.models import Sequential from keras.layers import Dense from keras.optimizers import Adam np.random.seed(0) """ data collection & preprocessing """ # number of points points = 500 # input data X = np.linspace(-3, 3, points) # signal # y = np.sin(X) # signal + noise # Adding noise on the sin signal to produce difficult data to the model to learn y = np.sin(X) + np.random.uniform(-0.5, 0.5, points) # print(X) # print(np.sin(X)) # print(np.random.uniform(-0.5, 0.5, points)) # print(y) # plt.scatter(X, y) """ create model FFN """ model = Sequential() # 1st hidden layer 50 nodes | 1 single input : price(size) : linear regrssion model.add(Dense(50, activation='sigmoid', input_dim=1)) # 2nd hidden layer 30 nodes | activation layer : sigmoid : simple linear model model.add(Dense(30, activation='sigmoid')) # output layer model.add(Dense(1)) # error optimizer : gradient descent Adam adam = Adam(lr=0.01) # mean square error = Moyenne Quadratique (fonction de coût) model.compile(loss='mse', optimizer=adam) """ train """ model.fit(X, y, epochs=50) """ predictions of estimated values """ predictions = model.predict(X) """print prediction """ plt.scatter(X, y) plt.plot(X, predictions, 'ro') plt.show()

Epoch 1/50
16/16 [==============================] - 1s 2ms/step - loss: 0.6277
Epoch 2/50
16/16 [==============================] - 0s 2ms/step - loss: 0.2549
Epoch 3/50
16/16 [==============================] - 0s 2ms/step - loss: 0.2490
Epoch 4/50
16/16 [==============================] - 0s 2ms/step - loss: 0.2187
Epoch 5/50
16/16 [==============================] - 0s 1ms/step - loss: 0.2276
Epoch 6/50
16/16 [==============================] - 0s 2ms/step - loss: 0.2295
Epoch 7/50
16/16 [==============================] - 0s 1ms/step - loss: 0.2294
Epoch 8/50
16/16 [==============================] - 0s 2ms/step - loss: 0.2085
Epoch 9/50
16/16 [==============================] - 0s 2ms/step - loss: 0.1957
Epoch 10/50
16/16 [==============================] - 0s 1ms/step - loss: 0.2095
Epoch 11/50
16/16 [==============================] - 0s 1ms/step - loss: 0.1868
Epoch 12/50
16/16 [==============================] - 0s 2ms/step - loss: 0.1655
Epoch 13/50
16/16 [==============================] - 0s 2ms/step - loss: 0.1549
Epoch 14/50
16/16 [==============================] - 0s 2ms/step - loss: 0.1554
Epoch 15/50
16/16 [==============================] - 0s 2ms/step - loss: 0.1351
Epoch 16/50
16/16 [==============================] - 0s 2ms/step - loss: 0.1389
Epoch 17/50
16/16 [==============================] - 0s 2ms/step - loss: 0.1342
Epoch 18/50
16/16 [==============================] - 0s 2ms/step - loss: 0.1194
Epoch 19/50
16/16 [==============================] - 0s 2ms/step - loss: 0.1273
Epoch 20/50
16/16 [==============================] - 0s 2ms/step - loss: 0.1124
Epoch 21/50
16/16 [==============================] - 0s 1ms/step - loss: 0.1185
Epoch 22/50
16/16 [==============================] - 0s 2ms/step - loss: 0.1347
Epoch 23/50
16/16 [==============================] - 0s 2ms/step - loss: 0.1123
Epoch 24/50
16/16 [==============================] - 0s 2ms/step - loss: 0.1149
Epoch 25/50
16/16 [==============================] - 0s 1ms/step - loss: 0.1266
Epoch 26/50
16/16 [==============================] - 0s 2ms/step - loss: 0.1090
Epoch 27/50
16/16 [==============================] - 0s 1ms/step - loss: 0.1233
Epoch 28/50
16/16 [==============================] - 0s 2ms/step - loss: 0.1093
Epoch 29/50
16/16 [==============================] - 0s 1ms/step - loss: 0.1073
Epoch 30/50
16/16 [==============================] - 0s 1ms/step - loss: 0.1103
Epoch 31/50
16/16 [==============================] - 0s 1ms/step - loss: 0.1070
Epoch 32/50
16/16 [==============================] - 0s 2ms/step - loss: 0.1147
Epoch 33/50
16/16 [==============================] - 0s 1ms/step - loss: 0.1097
Epoch 34/50
16/16 [==============================] - 0s 2ms/step - loss: 0.1107
Epoch 35/50
16/16 [==============================] - 0s 2ms/step - loss: 0.1042
Epoch 36/50
16/16 [==============================] - 0s 2ms/step - loss: 0.1098
Epoch 37/50
16/16 [==============================] - 0s 2ms/step - loss: 0.0981
Epoch 38/50
16/16 [==============================] - 0s 2ms/step - loss: 0.1146
Epoch 39/50
16/16 [==============================] - 0s 2ms/step - loss: 0.1050
Epoch 40/50
16/16 [==============================] - 0s 2ms/step - loss: 0.0945
Epoch 41/50
16/16 [==============================] - 0s 2ms/step - loss: 0.1033
Epoch 42/50
16/16 [==============================] - 0s 1ms/step - loss: 0.0997
Epoch 43/50
16/16 [==============================] - 0s 2ms/step - loss: 0.1050
Epoch 44/50
16/16 [==============================] - 0s 2ms/step - loss: 0.1161
Epoch 45/50
16/16 [==============================] - 0s 2ms/step - loss: 0.1097
Epoch 46/50
16/16 [==============================] - 0s 2ms/step - loss: 0.1117
Epoch 47/50
16/16 [==============================] - 0s 2ms/step - loss: 0.1066
Epoch 48/50
16/16 [==============================] - 0s 2ms/step - loss: 0.1037
Epoch 49/50
16/16 [==============================] - 0s 1ms/step - loss: 0.1092
Epoch 50/50
16/16 [==============================] - 0s 2ms/step - loss: 0.1075

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