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In [1]:

    
from keras.models import Sequential
from keras.layers import LSTM
import numpy as np









    



Using TensorFlow backend.



In [12]:

    
# 入力系列は長さ3だが、出力の系列は1（最後の入力に対してだけ出力する）
model = Sequential()
model.add(LSTM(5, input_shape=(3, 1)))
model.compile(optimizer='adam', loss='mse')

# input time steps
data = np.array([0.1, 0.2, 0.3]).reshape((1, 3, 1))
res = model.predict(data)
print(res)
print(res.shape)









    



[[-0.01279215 -0.02360711 -0.05856827 -0.01319192  0.03173996]]
(1, 5)



In [13]:

    
# LSTMをstackするには入力系列のそれぞれに対して出力する必要がある
# return_sequences=TrueとすればOK
model = Sequential()
model.add(LSTM(5, return_sequences=True, input_shape=(3, 1)))
model.compile(optimizer='adam', loss='mse')

data = np.array([0.1, 0.2, 0.3]).reshape((1, 3, 1))
res = model.predict(data)
print(res)
print(res.shape)









    



[[[-0.00477986 -0.00021732 -0.01271267  0.00416994 -0.00267648]
  [-0.01305808  0.00077787 -0.03372005  0.01082444 -0.0079989 ]
  [-0.02405662  0.00373452 -0.06012451  0.01877143 -0.01577036]]]
(1, 3, 5)

Sine Wave



In [16]:

    
from math import sin
from math import pi
import matplotlib.pyplot as plt
%matplotlib inline

length = 100
freq = 5
sequence = [sin(2 * pi * freq * (i / length)) for i in range(length)]

plt.plot(sequence)









    Out[16]:





[<matplotlib.lines.Line2D at 0x323122c18>]



In [17]:

    
from math import sin, pi, exp
import matplotlib.pyplot as plt

length = 100
period = 10
decay = 0.05
sequence = [0.5 + 0.5 * sin(2 * pi * i / period) * exp(-decay * i) for i in range(length)]

plt.plot(sequence)









    Out[17]:





[<matplotlib.lines.Line2D at 0x323187908>]



In [18]:

    
# generate damped sine wave in [0, 1]
def generate_sequence(length, period, decay):
    return [0.5 + 0.5 * sin(2 * pi * i / period) * exp(-decay * i) for i in range(length)]



In [19]:

    
seq = generate_sequence(100, 10, 0.05)
plt.plot(seq)









    Out[19]:





[<matplotlib.lines.Line2D at 0x3251a0780>]



In [21]:

    
seq = generate_sequence(100, 20, 0.05)
plt.plot(seq)









    Out[21]:





[<matplotlib.lines.Line2D at 0x325314a58>]



In [24]:

    
# generate input and output pairs of damped sine waves
import numpy as np
import random

def generate_examples(length, n_patterns, output):
    X, y = list(), list()
    for _ in range(n_patterns):
        p = random.randint(10, 20)  # period
        d = random.uniform(0.01, 0.1)  # decay
        sequence = generate_sequence(length + output, p, d)
        X.append(sequence[:-output])
        y.append(sequence[-output:])
    X = np.array(X).reshape(n_patterns, length, 1)  # (samples, time steps, features)の3Dテンソル
    y = np.array(y).reshape(n_patterns, output)
    return X, y



In [31]:

    
X, y = generate_examples(20, 5, 5)
for i in range(len(X)):
    plt.plot([x for x in X[i, :, 0]] + [x for x in y[i]], 'o-')



In [32]:

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

length = 50
output = 5  # 最後の5ステップの値を予測する

model = Sequential()
model.add(LSTM(20, return_sequences=True, input_shape=(length, 1)))
model.add(LSTM(20))
model.add(Dense(output))
model.compile(loss='mae', optimizer='adam')
model.summary()









    



_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
lstm_13 (LSTM)               (None, 50, 20)            1760      
_________________________________________________________________
lstm_14 (LSTM)               (None, 20)                3280      
_________________________________________________________________
dense_1 (Dense)              (None, 5)                 105       
=================================================================
Total params: 5,145
Trainable params: 5,145
Non-trainable params: 0
_________________________________________________________________

https://stackoverflow.com/questions/43882796/when-does-keras-reset-an-lstm-state
デフォルトではstateful = False
バッチごとにパラメータ更新時に内部状態が自動的にリセットされる
バッチ内の各シーケンス（サンプル）ごとに内部状態を 別々に 管理



In [34]:

    
# fit model
X, y = generate_examples(length, 10000, output)
history = model.fit(X, y, batch_size=10, epochs=1)









    



Epoch 1/1
10000/10000 [==============================] - 313s - loss: 0.0363



In [38]:

    
# evaluate model
X, y = generate_examples(length, 1000, output)
loss = model.evaluate(X, y, verbose=0)
print('MAE: %f' % loss)









    



MAE: 0.023665



In [79]:

    
# prediction on new data
X, y = generate_examples(length, 1, output)
yhat = model.predict(X, verbose=0)
X = X.reshape(50)
y = y.reshape(5)
yhat = yhat.reshape(5)
plt.plot(np.concatenate((X, y)), label='y')
plt.plot(np.concatenate((X, yhat)), label='yhat')
plt.legend()









    Out[79]:





<matplotlib.legend.Legend at 0x328b5fe80>

Vanilla LSTMの場合



In [97]:

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

length = 50
output = 5  # 最後の5ステップの値を予測する

model = Sequential()
model.add(LSTM(20, input_shape=(length, 1)))
model.add(Dense(output))
model.compile(loss='mae', optimizer='adam')
model.summary()

# fit model
X, y = generate_examples(length, 10000, output)
history = model.fit(X, y, batch_size=10, epochs=1)

# evaluate model
X, y = generate_examples(length, 1000, output)
loss = model.evaluate(X, y, verbose=0)
print('MAE: %f' % loss)









    



_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
lstm_18 (LSTM)               (None, 20)                1760      
_________________________________________________________________
dense_5 (Dense)              (None, 5)                 105       
=================================================================
Total params: 1,865
Trainable params: 1,865
Non-trainable params: 0
_________________________________________________________________
Epoch 1/1
10000/10000 [==============================] - 170s - loss: 0.0495   
MAE: 0.021882



In [105]:

    
# prediction on new data
X, y = generate_examples(length, 1, output)
yhat = model.predict(X, verbose=0)
X = X.reshape(50)
y = y.reshape(5)
yhat = yhat.reshape(5)
plt.plot(np.concatenate((X, y)), label='y')
plt.plot(np.concatenate((X, yhat)), label='yhat')
plt.legend()









    Out[105]:





<matplotlib.legend.Legend at 0x32c7a2cf8>



In [ ]: