python - 塑造 LSTM 的数据，并将密集层的输出馈送到 LSTM

Question

我正在尝试找出适合我想要拟合的模型的正确语法。这是一个时间序列预测问题，我想在将时间序列输入 LSTM 之前使用一些密集层来改进时间序列的表示。

这是我正在使用的虚拟系列:

import pandas as pd
import matplotlib.pyplot as plt
plt.style.use('seaborn-whitegrid')
import numpy as np
import keras as K
import tensorflow as tf

d = pd.DataFrame(data = {"x": np.linspace(0, 100, 1000)})
d['l1_x'] = d.x.shift(1)
d['l2_x'] = d.x.shift(2)
d.fillna(0, inplace = True)
d["y"] = np.sin(.1*d.x*np.sin(d.l1_x))*np.sin(d.l2_x)
plt.plot(d.x, d.y)

首先，我将拟合一个前面没有密集层的 LSTM。这需要我 reshape 数据:

X = d[["x", "l1_x", "l2_x"]].values.reshape(len(d), 3,1)
y = d.y.values

这是正确的吗？

这些教程看起来单个时间序列的第一维应为 1，后跟时间步数 (1000)，最后是协变量数 (3)。但是当我这样做时，模型无法编译。

这里我编译并训练模型:

model = K.Sequential()
model.add(K.layers.LSTM(10, input_shape=(X.shape[1], X.shape[2]), batch_size = 1, stateful=True))
model.add(K.layers.Dense(1))
callbacks = [K.callbacks.EarlyStopping(monitor='loss', min_delta=0, patience=5, verbose=1, mode='auto', baseline=None, restore_best_weights=True)]
model.compile(loss='mean_squared_error', optimizer='rmsprop')

model.fit(X, y, epochs=50, batch_size=1, verbose=1, shuffle=False, callbacks = callbacks)
model.reset_states()

yhat = model.predict(X, 1)
plt.clf()
plt.plot(d.x, d.y)
plt.plot(d.x, yhat)

为什么我无法让模型过度拟合？是因为我错误地重新调整了数据吗？当我在 LSTM 中使用更多节点时，它并没有真正变得更加过度拟合。

(我也不清楚“有状态”是什么意思。神经网络只是非线性模型。“状态”指的是哪些参数以及为什么要重置它们？)

如何在输入和 LSTM 之间插入密集层？ 最后，我想添加一堆密集层，基本上在到达 LSTM 之前对 x 进行基础扩展。但 LSTM 需要 3D 数组和密集层输出矩阵。我在这里做什么？这不起作用:

model = K.Sequential()
model.add(K.layers.Dense(10, activation = "relu", input_dim = 3))
model.add(K.layers.LSTM(3, input_shape=(10, X.shape[2]), batch_size = 1, stateful=True))
model.add(K.layers.Dense(1))

ValueError: Input 0 is incompatible with layer lstm_2: expected ndim=3, found ndim=2

Answer 1

对于第一个问题，我正在做同样的事情，我没有收到任何错误，请分享您的错误。

注意:我将给你使用函数式 API 的示例，这给了你更多的自由(个人意见)

from keras.layers import Dense, Flatten, LSTM, Activation
from keras.layers import Dropout, RepeatVector, TimeDistributed
from keras import Input, Model

seq_length = 15
input_dims = 10
output_dims = 8
n_hidden = 10
model1_inputs = Input(shape=(seq_length,input_dims,))
model1_outputs = Input(shape=(output_dims,))

net1 = LSTM(n_hidden, return_sequences=True)(model1_inputs)
net1 = LSTM(n_hidden, return_sequences=False)(net1)
net1 = Dense(output_dims, activation='relu')(net1)
model1_outputs = net1

model1 = Model(inputs=model1_inputs, outputs = model1_outputs, name='model1')

## Fit the model
model1.summary()


_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
input_11 (InputLayer)        (None, 15, 10)            0         
_________________________________________________________________
lstm_8 (LSTM)                (None, 15, 10)            840       
_________________________________________________________________
lstm_9 (LSTM)                (None, 10)                840       
_________________________________________________________________
dense_9 (Dense)              (None, 8)                 88        
_________________________________________________________________

对于你的第二个问题，有两种方法:

1. 如果您发送数据时没有进行序列化，其尺寸为(batch, input_dims)，那么可以使用此方法 RepeatVector ，它通过 n_steps 重复相同的权重，这只不过是 LSTM 中的 rolling_steps。

{

seq_length = 15
input_dims = 16
output_dims = 8
n_hidden = 20
lstm_dims = 10
model1_inputs = Input(shape=(input_dims,))
model1_outputs = Input(shape=(output_dims,))

net1 = Dense(n_hidden)(model1_inputs)
net1 = Dense(n_hidden)(net1)

net1 = RepeatVector(3)(net1)
net1 = LSTM(lstm_dims, return_sequences=True)(net1)
net1 = LSTM(lstm_dims, return_sequences=False)(net1)
net1 = Dense(output_dims, activation='relu')(net1)
model1_outputs = net1

model1 = Model(inputs=model1_inputs, outputs = model1_outputs, name='model1')

## Fit the model
model1.summary()

_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
input_13 (InputLayer)        (None, 16)                0         
_________________________________________________________________
dense_13 (Dense)             (None, 20)                340       
_________________________________________________________________
dense_14 (Dense)             (None, 20)                420       
_________________________________________________________________
repeat_vector_2 (RepeatVecto (None, 3, 20)             0         
_________________________________________________________________
lstm_14 (LSTM)               (None, 3, 10)             1240      
_________________________________________________________________
lstm_15 (LSTM)               (None, 10)                840       
_________________________________________________________________
dense_15 (Dense)             (None, 8)                 88        
=================================================================

如果您要发送 Dim 序列 (seq_len, input_dims)，那么您可以 TimeDistributed ，它在整个序列上重复相同的密集层权重。

{

seq_length = 15
input_dims = 10
output_dims = 8
n_hidden = 10
lstm_dims = 6
model1_inputs = Input(shape=(seq_length,input_dims,))
model1_outputs = Input(shape=(output_dims,))

net1 = TimeDistributed(Dense(n_hidden))(model1_inputs)
net1 = LSTM(output_dims, return_sequences=True)(net1)
net1 = LSTM(output_dims, return_sequences=False)(net1)
net1 = Dense(output_dims, activation='relu')(net1)
model1_outputs = net1

model1 = Model(inputs=model1_inputs, outputs = model1_outputs, name='model1')

## Fit the model
model1.summary()


_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
input_17 (InputLayer)        (None, 15, 10)            0         
_________________________________________________________________
time_distributed_3 (TimeDist (None, 15, 10)            110       
_________________________________________________________________
lstm_18 (LSTM)               (None, 15, 8)             608       
_________________________________________________________________
lstm_19 (LSTM)               (None, 8)                 544       
_________________________________________________________________
dense_19 (Dense)             (None, 8)                 72        
=================================================================

注意:我堆叠了两层，这样做时，在第一层中我使用了return_sequence，它返回每个时间步骤的输出，由第二层使用层，仅在最后一个 time_step 返回输出。