LSTM 序列到序列(seq to seq)问题建模, 根据问题和数据本身的特点,可以分为几种不同:
- 一对一(one to one)
- 多对一(many to one)
- 一对多(one to many)
- 多对多(many to many)
(1) 一对一(one to one)
这种模型是根据过去的一个时间点上的数据,预测下一个时间点的数据. 典型的问题结构是:
y(t+1) = f(x(t))
对应的LSTM网络结构是:
按照timestep展开后, 网络结构如下:
一对一模型用keras建模实现如下:
model = Sequential()
model.add(LSTM(..., input_shape=(1, features)))
model.add(Dense(1))值得注意的是, 数据本身可以是一个向量, 也就是说, 在一个时间点上, 对应的数据本身是多维的.
整个网络的输入是1个长度为features的向量， 输出是标量。
(2) 多对一(many to one)
此时,网络输入的时间步是大于1的, 但是输出的预测时间步只是1.
y(t+1) = f(x(t-n), x(t-n+1), …, x(t))
此时的网络结构为:
model = Sequential()
features = 10
vectors = 3
model.add(LSTM(8, input_shape=(vectors, features)))
model.add(Dense(1))
print(model.summary())可以得到：
_________________________________________________________________
Layer (type) Output Shape Param #
=================================================================
lstm_27 (LSTM) (None, 8) 608
_________________________________________________________________
dense_22 (Dense) (None, 1) 9
=================================================================
Total params: 617
Trainable params: 617
Non-trainable params: 0
_________________________________________________________________
NoneTimeDistributed()包装器
要输出对未来多个时间步上的预测, 就必须使用TimeDistributed()包装器, 将输出上一层网络的输出在时间轴上展开. 关于TimeDistributed()包装器, F. Chollet(Keras的作者)解释说：
TimeDistributedDense将同样的密集(全连接)操作应用到3D张量的每一个时间间隔上。
TimeDistributedDense applies a same Dense (fully-connected) operation to every timestep of a 3D tensor.
这一点可以用一个简单的例子说明. 例如如下的单层LSTM网络:
model = Sequential()
model.add(LSTM(1, input_shape=(10,1)))
print(model.summary())得到:
_________________________________________________________________
Layer (type) Output Shape Param #
=================================================================
lstm_15 (LSTM) (None, 1) 12
=================================================================
Total params: 12
Trainable params: 12
Non-trainable params: 0
_________________________________________________________________
None另外一个单层LSTM网络外面还增加了TimeDistributed()包装器.
model = Sequential()
model.add(TimeDistributed(LSTM(1, input_shape=(None, 10, 1))))
print(model.summary())得到:
_________________________________________________________________
Layer (type) Output Shape Param #
=================================================================
time_distributed_14 (TimeDis (None, None, 1) 12
=================================================================
Total params: 12
Trainable params: 12
Non-trainable params: 0
_________________________________________________________________
None得到的网络参数都是12. 可见, TimeDistributed()包装器没有引入新的参数, 而是将同样的网络分别在batch中的每个样本上都应用了.正如这个包装器的命名，是将训练数据的batch视为在时间轴上的展开. 这一点上可以从Output Shape中看出来。 对于第一个单层LSTM网络，输出的数据维度就是[batch, 1], 第二个LSTM网络的输出是[batch, batch, 1].
有了对TimeDistributed()包装器的基本认识，我们就可以理解下面的多时间步预测问题。
(3) 一对多(one to many)
这种问题的典型结构是:
y(t+1), y(t+2) = f(x(t))
也就是说, 根据过去一步的数据, 预测未来两步的数据. 用keras建模应该是:
model = Sequential()
features = 8
model.add(LSTM(out_dim, input_shape(1, features), return_sequences=True))
model.add(TimeDistributed(Dense(1)))这里TimeDistributed() 包装器将第一层LSTM的输出序列按照时间顺序排列好. 例如上面LSTM网络的输入数据是[batch, 1, features], 那么输出是: [batch, 1, 20]
在Dense层，增加了TimeDistributed()包装器，可以得到输出的维数是：[batch, 1, 1]
这个模型的结构和输出数据的维数是：
_________________________________________________________________
Layer (type) Output Shape Param #
=================================================================
lstm_18 (LSTM) (None, 1, 20) 2320
_________________________________________________________________
time_distributed_17 (TimeDis (None, 1, 1) 21
=================================================================
Total params: 2,341
Trainable params: 2,341
Non-trainable params: 0
_________________________________________________________________
None
output_shape is : (None, 1, 1)网络的输入是1个长度是8维的向量，输出是标量。
(4) 多对多(many to many)
多对多问题的典型结构是：
y(t+1), y(t+2), …, y(t+n) = f(y(t-n), y(t-n+1), …, y(t))
用keras建模：
from keras.models import Sequential
from keras.layers import LSTM, Dense, TimeDistributed
model = Sequential()
in_features = 8
n_in = 10
out_dim = 6
out_features = 12
model.add(LSTM(out_dim, input_shape=(n_in, in_features), return_sequences=True))
model.add(TimeDistributed(Dense(out_features)))
print(model.summary())得到：
Using TensorFlow backend.
_________________________________________________________________
Layer (type) Output Shape Param #
=================================================================
lstm_1 (LSTM) (None, 10, 6) 360
_________________________________________________________________
time_distributed_1 (TimeDist (None, 10, 12) 84
=================================================================
Total params: 444
Trainable params: 444
Non-trainable params: 0
_________________________________________________________________
None
网络的输入是10个长度为8的向量，输出是长度是12的向量。
如果输入序列的长度与输出序列不一致, 那么需要在网络中增加RepeatVector()层.
from keras.layers import RepeatVector
model = Sequential()
n_in = 120
n_out = 60
model.add(LSTM(60, input_shape=(n_in, 1)))
model.add(RepeatVector(n_out))
model.add(LSTM(20, return_sequences=True))
model.add(TimeDistributed(Dense(1)))
model.compile(loss='mse', optimizer='adam')
print(model.summary()) 得到:
_________________________________________________________________
Layer (type) Output Shape Param #
=================================================================
lstm_4 (LSTM) (None, 60) 14880
_________________________________________________________________
repeat_vector_1 (RepeatVecto (None, 60, 60) 0
_________________________________________________________________
lstm_5 (LSTM) (None, 60, 20) 6480
_________________________________________________________________
time_distributed_2 (TimeDist (None, 60, 1) 21
=================================================================
Total params: 21,381
Trainable params: 21,381
Non-trainable params: 0
_________________________________________________________________
None