极差的预测：LSTM 时间序列

Question

我尝试实现 LSTM 模型进行时间序列预测。下面是我的试用代码。此代码运行没有错误。您也可以在不依赖的情况下尝试。

import numpy as np, pandas as pd, matplotlib.pyplot as plt
from sklearn.preprocessing import MinMaxScaler
from keras.models import Sequential
from keras.layers import LSTM, Dense, TimeDistributed, Bidirectional
from sklearn.metrics import mean_squared_error, accuracy_score
from scipy.stats import linregress
from sklearn.utils import shuffle

fi = 'pollution.csv'
raw = pd.read_csv(fi, delimiter=',')
raw = raw.drop('Dates', axis=1)
print (raw.shape)

scaler = MinMaxScaler(feature_range=(-1, 1))
raw = scaler.fit_transform(raw)

time_steps = 7
def create_ds(data, t_steps):
    data = pd.DataFrame(data)
    data_s = data.copy()
    for i in range(time_steps):
        data = pd.concat([data, data_s.shift(-(i+1))], axis = 1)   
    data.dropna(axis=0, inplace=True)
    return data.values

ds = create_ds(raw, time_steps)
print (ds.shape)
n_feats = raw.shape[1]
n_obs = time_steps * n_feats

n_rows = ds.shape[0]
train_size = int(n_rows * 0.8)

train_data = ds[:train_size, :]
train_data = shuffle(train_data)

test_data = ds[train_size:, :]

x_train = train_data[:, :n_obs]
y_train = train_data[:, n_obs:]
x_test = test_data[:, :n_obs]
y_test = test_data[:, n_obs:]

x_train = x_train.reshape(1, x_train.shape[0], x_train.shape[1])
y_train = y_train.reshape(1, y_train.shape[0], y_train.shape[1])
x_test = x_test.reshape(1, x_test.shape[0], x_test.shape[1])

print (x_train.shape)
print (y_train.shape)
print (x_test.shape)
print (y_test.shape)

model = Sequential()
model.add(LSTM(64, return_sequences=True, input_shape=(None, x_train.shape[2]), stateful=True, batch_size=1))
model.add(LSTM(32, return_sequences=True, stateful=True))
model.add(LSTM(n_feats, return_sequences=True, stateful=True)) 

model.compile(loss='mse', optimizer='rmsprop')
model.fit(x_train, y_train, epochs=10, batch_size=1, verbose=2)  
y_predict = model.predict(x_test)
y_predict = y_predict.reshape(y_predict.shape[1], y_predict.shape[2])

y_predict = scaler.inverse_transform(y_predict)

y_test = scaler.inverse_transform(y_test)
y_test = y_test[:,0]
y_predict = y_predict[:,0]

print (y_test.shape)
print (y_predict.shape)

plt.plot(y_test, label='True')
plt.plot(y_predict,  label='Predict')
plt.legend()
plt.show()

但是，预测非常差。如何提高预测能力？你有什么想法可以改进它吗？

通过重新设计架构和/或层来改进预测的任何想法？

Answer 1

如果你想在我的代码中使用模型（你传递的链接），你需要正确塑造数据：（1个序列，total_time_steps，5个特征）

重要提示：我不知道这是最好的方法还是最好的模型，但该模型预测输入 ( time_shift=7)之前的 7 个时间步

数据和初始变量

    fi = 'pollution.csv'
raw = pd.read_csv(fi, delimiter=',')
raw = raw.drop('Dates', axis=1)
print("raw shape:")
print (raw.shape)
#(1789,5) - 1789 time steps / 5 features

scaler = MinMaxScaler(feature_range=(-1, 1))
raw = scaler.fit_transform(raw)

time_shift = 7 #shift is the number of steps we are predicting ahead
n_rows = raw.shape[0] #n_rows is the number of time steps of our sequence
n_feats = raw.shape[1]
train_size = int(n_rows * 0.8)


#I couldn't understand how "ds" worked, so I simply removed it because in the code below it's not necessary

#getting the train part of the sequence
train_data = raw[:train_size, :] #first train_size steps, all 5 features
test_data = raw[train_size:, :] #I'll use the beginning of the data as state adjuster


#train_data = shuffle(train_data) !!!!!! we cannot shuffle time steps!!! we lose the sequence doing this

x_train = train_data[:-time_shift, :] #the entire train data, except the last shift steps 
x_test = test_data[:-time_shift,:] #the entire test data, except the last shift steps
x_predict = raw[:-time_shift,:] #the entire raw data, except the last shift steps

y_train = train_data[time_shift:, :] 
y_test = test_data[time_shift:,:]
y_predict_true = raw[time_shift:,:]

x_train = x_train.reshape(1, x_train.shape[0], x_train.shape[1]) #ok shape (1,steps,5) - 1 sequence, many steps, 5 features
y_train = y_train.reshape(1, y_train.shape[0], y_train.shape[1])
x_test = x_test.reshape(1, x_test.shape[0], x_test.shape[1])
y_test = y_test.reshape(1, y_test.shape[0], y_test.shape[1])
x_predict = x_predict.reshape(1, x_predict.shape[0], x_predict.shape[1])
y_predict_true = y_predict_true.reshape(1, y_predict_true.shape[0], y_predict_true.shape[1])

print("\nx_train:")
print (x_train.shape)
print("y_train")
print (y_train.shape)
print("x_test")
print (x_test.shape)
print("y_test")
print (y_test.shape)

模型

你的模型对于这个任务不是很强大，所以我尝试了一个更大的模型（另一方面这个太强大了）

model = Sequential()
model.add(LSTM(64, return_sequences=True, input_shape=(None, x_train.shape[2])))
model.add(LSTM(128, return_sequences=True))
model.add(LSTM(256, return_sequences=True))
model.add(LSTM(128, return_sequences=True))
model.add(LSTM(64, return_sequences=True))
model.add(LSTM(n_feats, return_sequences=True)) 

model.compile(loss='mse', optimizer='adam')

配件

请注意，我必须训练 2000 多个 epoch 才能使模型获得良好的结果。
我添加了验证数据，以便我们可以比较训练和测试的损失。

#notice that I'm predicting from the ENTIRE sequence, including x_train      
#is important for the model to adjust its states before predicting the end
model.fit(x_train, y_train, epochs=1000, batch_size=1, verbose=2, validation_data=(x_test,y_test))  

预测

重要提示：至于根据开头预测序列的结尾，重要的是模型看到开头以调整内部状态，因此我预测的是整个数据 ( x_predict)，而不仅仅是测试数据。

y_predict_model = model.predict(x_predict)

print("\ny_predict_true:")
print (y_predict_true.shape)
print("y_predict_model: ")
print (y_predict_model.shape)


def plot(true, predicted, divider):

    predict_plot = scaler.inverse_transform(predicted[0])
    true_plot = scaler.inverse_transform(true[0])

    predict_plot = predict_plot[:,0]
    true_plot = true_plot[:,0]

    plt.figure(figsize=(16,6))
    plt.plot(true_plot, label='True',linewidth=5)
    plt.plot(predict_plot,  label='Predict',color='y')

    if divider > 0:
        maxVal = max(true_plot.max(),predict_plot.max())
        minVal = min(true_plot.min(),predict_plot.min())

        plt.plot([divider,divider],[minVal,maxVal],label='train/test limit',color='k')

    plt.legend()
    plt.show()

test_size = n_rows - train_size
print("test length: " + str(test_size))

plot(y_predict_true,y_predict_model,train_size)
plot(y_predict_true[:,-2*test_size:],y_predict_model[:,-2*test_size:],test_size)

显示整个数据

显示它的结尾部分以获取更多详细信息

请注意，这个模型是过拟合的，这意味着它可以学习训练数据并在测试数据中得到不好的结果。

为了解决这个问题，你必须通过实验尝试更小的模型，使用 dropout 层和其他技术来防止过度拟合。

另请注意，此数据很可能包含大量随机因素，这意味着模型将无法从中学习任何有用的信息。当您制作较小的模型以避免过度拟合时，您可能还会发现模型对训练数据的预测更差。

找到完美的模型并非易事，这是一个悬而未决的问题，您必须进行实验。也许 LSTM 模型根本不是解决方案。也许您的数据根本无法预测，等等。对此没有明确的答案。

如何知道模型好不好

使用训练中的验证数据，您可以比较训练和测试数据的损失。

Train on 1 samples, validate on 1 samples
Epoch 1/1000
9s - loss: 0.4040 - val_loss: 0.3348
Epoch 2/1000
4s - loss: 0.3332 - val_loss: 0.2651
Epoch 3/1000
4s - loss: 0.2656 - val_loss: 0.2035
Epoch 4/1000
4s - loss: 0.2061 - val_loss: 0.1696
Epoch 5/1000
4s - loss: 0.1761 - val_loss: 0.1601
Epoch 6/1000
4s - loss: 0.1697 - val_loss: 0.1476
Epoch 7/1000
4s - loss: 0.1536 - val_loss: 0.1287
Epoch 8/1000
.....

两者应该一起下去。当测试数据停止下降，但训练数据继续改善时，您的模型开始过度拟合。

尝试其他模型

我能做的最好的事情（但我并没有真正尝试太多）是使用这个模型：

model = Sequential()
model.add(LSTM(64, return_sequences=True, input_shape=(None, x_train.shape[2])))
model.add(LSTM(128, return_sequences=True))
model.add(LSTM(128, return_sequences=True))
model.add(LSTM(64, return_sequences=True))
model.add(LSTM(n_feats, return_sequences=True)) 

model.compile(loss='mse', optimizer='adam')

当损失大约是：

loss: 0.0389 - val_loss: 0.0437

在这一点之后，验证损失开始上升（因此超出这一点的训练完全没有用）

结果：

这表明该模型可以学习的只是非常全面的行为，例如具有较高值的​​区域。

但是高频要么太随机，要么模型不够好……

Answer 2

您可以考虑更改您的模型：

import numpy as np, pandas as pd, matplotlib.pyplot as plt
from sklearn.preprocessing import MinMaxScaler
from keras.models import Sequential
from keras.layers import LSTM, Dense, TimeDistributed, Bidirectional
from sklearn.metrics import mean_squared_error, accuracy_score
from scipy.stats import linregress
from sklearn.utils import shuffle

fi = 'pollution.csv'
raw = pd.read_csv(fi, delimiter=',')
raw = raw.drop('Dates', axis=1)
print (raw.shape)

scaler = MinMaxScaler(feature_range=(-1, 1))
raw = scaler.fit_transform(raw)

time_steps = 7
def create_ds(data, t_steps):
    data = pd.DataFrame(data)
    data_s = data.copy()
    for i in range(time_steps):
        data = pd.concat([data, data_s.shift(-(i+1))], axis = 1)   
    data.dropna(axis=0, inplace=True)
    return data.values

ds = create_ds(raw, time_steps)
print (ds.shape)
n_feats = raw.shape[1]
n_obs = time_steps * n_feats

n_rows = ds.shape[0]
train_size = int(n_rows * 0.8)

train_data = ds[:train_size, :]
train_data = shuffle(train_data)

test_data = ds[train_size:, :]

x_train = train_data[:, :n_obs]
y_train = train_data[:, n_obs:]
x_test = test_data[:, :n_obs]
y_test = test_data[:, n_obs:]

print (x_train.shape)
print (x_test.shape)
print (y_train.shape)
print (y_test.shape)

x_train = x_train.reshape(x_train.shape[0], time_steps, n_feats)
x_test = x_test.reshape(x_test.shape[0], time_steps, n_feats)

print (x_train.shape)
print (x_test.shape)
print (y_train.shape)
print (y_test.shape)

model = Sequential()
model.add(LSTM(64, input_shape=(time_steps, n_feats), return_sequences=True))
model.add(LSTM(32, return_sequences=False))
model.add(Dense(n_feats))

model.compile(loss='mse', optimizer='rmsprop')
model.fit(x_train, y_train, epochs=10, batch_size=1, verbose=1, shuffle=False)

y_predict = model.predict(x_test)
print (y_predict.shape)
y_predict = scaler.inverse_transform(y_predict)

y_test = scaler.inverse_transform(y_test)
y_test = y_test[:,0]
y_predict = y_predict[:,0]

print (y_test.shape)
print (y_predict.shape)

plt.plot(y_test, label='True')
plt.plot(y_predict,  label='Predict')
plt.legend()
plt.show()

但我真的不知道你的实施的优点：

* both x and y are 3d (1,steps,features) rather than x in 3d (samples, time-steps, features) and y in 2d (samples, features)
* input_shape=(None, x_train.shape[2])
* last layer - model.add(LSTM(n_feats, return_sequences=True, stateful=True)) 

有人可能会提供更好的答案。