为什么模型甚至无法预测正弦

Question

我正在尝试使用 Keras 生成具有 LSTM RNN 的学习时间序列，因此我想预测一个数据点，并将其作为输入反馈回来以预测下一个等等，这样我就可以实际生成时间序列（例如给定 2000 个数据点，预测下一个 2000） 我是这样试的，但是Test score RMSE是1.28，预测基本是一条直线

# LSTM for international airline passengers problem with regression framing
import numpy
import matplotlib.pyplot as plt
from pandas import read_csv
import math
from keras.models import Sequential
from keras.layers import Dense
from keras.layers import LSTM
from sklearn.preprocessing import MinMaxScaler
from sklearn.metrics import mean_squared_error
# convert an array of values into a dataset matrix
def create_dataset(dataset, look_back=1):
    dataX, dataY = [], []
    for i in range(len(dataset)-look_back-1):
        a = dataset[i:(i+look_back), 0]
        dataX.append(a)
        dataY.append(dataset[i + look_back, 0])
    return numpy.array(dataX), numpy.array(dataY)
# fix random seed for reproducibility
numpy.random.seed(7)

# load the dataset
dataset = np.sin(np.linspace(0,35,10000)).reshape(-1,1)
print(type(dataset))
print(dataset.shape)
dataset = dataset.astype('float32')

# normalize the dataset
scaler = MinMaxScaler(feature_range=(0, 1))
dataset = scaler.fit_transform(dataset)

# split into train and test sets
train_size = int(len(dataset) * 0.5)
test_size = len(dataset) - train_size
train, test = dataset[0:train_size,:], dataset[train_size:len(dataset),:]

# reshape into X=t and Y=t+1
look_back = 1
trainX, trainY = create_dataset(train, look_back)
testX, testY = create_dataset(test, look_back)
# reshape input to be [samples, time steps, features]
trainX = numpy.reshape(trainX, (trainX.shape[0], 1, trainX.shape[1]))
testX = numpy.reshape(testX, (testX.shape[0], 1, testX.shape[1]))

# create and fit the LSTM network
model = Sequential()
model.add(LSTM(16, input_shape=(1, look_back)))
model.add(Dense(1))
model.compile(loss='mean_squared_error', optimizer='adam')
model.fit(trainX, trainY, epochs=10, batch_size=1, verbose=2)

# make predictions
trainPredict = model.predict(trainX)
testPredict = list()
prediction = model.predict(testX[0].reshape(1,1,1))
for i in range(trainX.shape[0]):
    prediction = model.predict(prediction.reshape(1,1,1))
    testPredict.append(prediction)
testPredict = np.array(testPredict).reshape(-1,1)

# invert predictions
trainPredict = scaler.inverse_transform(trainPredict)
trainY = scaler.inverse_transform([trainY])
testPredict = scaler.inverse_transform(testPredict)
testY = scaler.inverse_transform([testY])

# calculate root mean squared error
trainScore = math.sqrt(mean_squared_error(trainY[0], trainPredict[:,0]))
print('Train Score: %.2f RMSE' % (trainScore))
testScore = math.sqrt(mean_squared_error(testY[0], testPredict[:,0]))
print('Test Score: %.2f RMSE' % (testScore))
# shift train predictions for plotting
trainPredictPlot = numpy.empty_like(dataset)
trainPredictPlot[:, :] = numpy.nan
trainPredictPlot[look_back:len(trainPredict)+look_back, :] = trainPredict
# shift test predictions for plotting
testPredictPlot = numpy.empty_like(dataset)
testPredictPlot[:, :] = numpy.nan
testPredictPlot[len(trainPredict)+(look_back*2)+1:len(dataset)-1, :] = testPredict

# plot baseline and predictions
plt.plot(scaler.inverse_transform(dataset))
plt.plot(trainPredictPlot)
plt.plot(testPredictPlot)
plt.show()

我做错了什么？

Answer 1

我发现您的代码存在多个问题。 look_back 的值为 1，这意味着 LSTM 一次只能看到一个 Sample，这显然不足以了解有关序列的任何信息。

您可能这样做是为了在最后做出最终预测，方法是将上一步的预测作为新输入。正确的方法是使用更多时间步进行训练，然后将网络更改为具有单个时间步的有状态 LSTM。

此外，当您进行最终预测时，您必须向网络展示多个真实样本。否则，正弦上的位置是不明确的。 （下一步是涨还是跌？）

我打了一个快速的例子。以下是我生成数据的方式：

import numpy as np

numSamples = 1000
numTimesteps = 50
width = np.pi/2.0

def getRandomSine(numSamples = 100, width = np.pi):
    return np.sin(np.linspace(0,width,numSamples) + (np.random.rand()*np.pi*2))

trainX = np.stack([getRandomSine(numSamples = numTimesteps+1) for _ in range(numSamples)])
valX = np.stack([getRandomSine(numSamples = numTimesteps+1) for _ in range(numSamples)])

trainX = trainX.reshape((numSamples,numTimesteps+1,1))
valX = valX.reshape((numSamples,numTimesteps+1,1))

trainY = trainX[:,1:,:]
trainX = trainX[:,:-1,:]

valY = valX[:,1:,:]
valX = valX[:,:-1,:]

在这里我训练了模型：

import keras
from keras.models import Sequential
from keras import layers


model = Sequential()
model.add(layers.recurrent.LSTM(32,return_sequences=True,input_shape=(numTimesteps, 1)))
model.add(layers.recurrent.LSTM(32,return_sequences=True))
model.add(layers.wrappers.TimeDistributed(layers.Dense(1,input_shape=(1,10))))
model.compile(loss='mean_squared_error',
              optimizer='adam')
model.summary()

model.fit(trainX, trainY, nb_epoch=50, validation_data=(valX, valY), batch_size=32)

在这里我更改了训练模型以允许继续预测：

# serialize the model and get its weights, for quick re-building
config = model.get_config()
weights = model.get_weights()

config[0]['config']['batch_input_shape'] = (1, 1, 1)
config[0]['config']['stateful'] = True
config[1]['config']['stateful'] = True

from keras.models import model_from_config
new_model = Sequential().from_config(config)
new_model.set_weights(weights)

#create test sine
testX = getRandomSine(numSamples = numTimesteps*10, width = width*10)

new_model.reset_states()
testPredictions = []
# burn in
for i in range(numTimesteps):
    prediction = new_model.predict(np.array([[[testX[i]]]]))
    testPredictions.append(prediction[0,0,0])

# prediction
for i in range(numTimesteps, len(testX)):
    prediction = new_model.predict(prediction)
    testPredictions.append(prediction[0,0,0])

# plot result
import matplotlib.pyplot as plt
plt.plot(np.stack([testPredictions,testX]).T)
plt.show()

这是结果的样子。预测误差加起来很快就偏离了输入正弦。但它清楚地了解了正弦的一般形状。您现在可以尝试通过尝试不同的层、激活函数等来改进这一点。

Answer 2

我正在研究不同的架构and uploaded it on github.

因此，对于所有正在研究逐点预测时间序列的人，我希望这会有所帮助。

结果如下所示：