Function Inference

Sin Function



In [3]:

    
from keras.models import Sequential
from keras.layers import LSTM, Dense

import numpy as np
import math
%matplotlib inline
import matplotlib.pyplot as plt

model = Sequential()
model.add(Dense(100, input_dim=1, init='uniform',activation='relu'))
model.add(Dense(50, activation='relu'))
model.add(Dense(50, activation='relu'))
model.add(Dense(1, activation='tanh'))
model.compile(loss='mean_squared_error',optimizer='rmsprop',metrics=['accuracy'])

x_train = 2*math.pi*np.random.random((5000,1))
y_train = np.sin(x_train)

x_val = 2*math.pi*np.random.random((100,1))
y_val = np.sin(x_val)

model.fit(x_train,y_train, nb_epoch=100, batch_size=20,verbose=0,shuffle=True, validation_split=0.2)









    Out[3]:





<keras.callbacks.History at 0x71bbaef0>

Prediction



In [4]:

    
out = model.predict(x_val)

Comparsion



In [5]:

    
plt.scatter(x_val, y_val,c='r',label='Accurate')
plt.scatter(x_val,out,label='Predicted')
plt.legend(loc=1)
plt.show()

Extension



In [6]:

    
x_ext = 6*math.pi*np.random.random((100,1))
out = model.predict(x_ext)
plt.scatter(x_ext,out,label='Predicted')
plt.legend(loc=1)
plt.show()

Linear Function



In [9]:

    
from keras.models import Sequential
from keras.layers import LSTM, Dense

import numpy as np
import math
%matplotlib inline
import matplotlib.pyplot as plt

model = Sequential()
model.add(Dense(100, input_dim=1, init='uniform',activation='relu'))
model.add(Dense(50, activation='relu'))
model.add(Dense(50, activation='relu'))
model.add(Dense(1, activation='linear'))
model.compile(loss='mean_squared_error',optimizer='rmsprop',metrics=['accuracy'])

x_train = 100*np.random.random((5000,1))
y_train = 50 + 0.2*x_train

x_val = 100*np.random.random((100,1))
y_val = 50 + 0.2*x_val

hist = model.fit(x_train,y_train, nb_epoch=100, batch_size=20,verbose=0,shuffle=True, validation_split=0.2)

out = model.predict(x_val)

plt.scatter(x_val, y_val,c='r',label='Accurate')
plt.scatter(x_val,out,label='Predicted')
plt.legend(loc=1)
plt.show()

Nonlinear Function



In [16]:

    
from keras.models import Sequential
from keras.layers import LSTM, Dense

import numpy as np
import math
%matplotlib inline
import matplotlib.pyplot as plt

model = Sequential()
model.add(Dense(100, input_dim=1, init='uniform',activation='linear'))
model.add(Dense(50, activation='relu'))
model.add(Dense(50, activation='linear'))
model.add(Dense(1, activation='linear'))
model.compile(loss='mean_squared_error',optimizer='rmsprop',metrics=['accuracy'])

x_train = 2*math.pi*np.random.random((5000,1))
y_train = 50*np.exp(np.sin(x_train))

x_val = 2*math.pi*np.random.random((100,1))
y_val = 50*np.exp(np.sin(x_val))

hist = model.fit(x_train,y_train, nb_epoch=200, batch_size=40,verbose=0,shuffle=True, validation_split=0.1)

out = model.predict(x_val)

plt.scatter(x_val, y_val,c='r',label='Accurate')
plt.scatter(x_val,out,label='Predicted')
plt.legend(loc=1)
plt.show()

Adjustable parameters

Type of Neural Network
Node number, Initilization, Activation Form, Dropout of each layer
Loss function, Optimizer type, Metrics function to compile network
Epoch, BatchSize, Shuffle, Validation Setting to fit data



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