所以我一直在对一个数据集使用一些不同的预测方法，我过去做过一些更基本的分析。无需赘述，它是由各种未知因素驱动的一段时间内的人口数据。我不希望能够很好地预测它，而且，从历史上看，我使用 ARIMA 等更幼稚的模型看到 MAPE 值在 25% 范围内（尽管即使是 Prophet 模型也效果不佳）。所以今天，为了好玩，我决定尝试来自https://machinelearningmastery.com/time-series-prediction-lstm-recurrent-neural-networks-python-keras/的 LSTM 代码看看它会怎么做。可以说，它表现得太好了。好吧，我假设我做错了什么。为了好玩，我决定将参数的数量限制为尽可能少的数量。这个模型实际上有 9 个参数：
我在 LSTM 和 Dense 层上禁用了偏置参数，并指定了一个线性激活函数。我认为 LSTM+Dense 不可能使用更少的参数。
为了使模型更难，我将其训练了 1 步并将回溯设置为 1。生成的代码如下所示：
# LSTM for international airline passengers problem with memory
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(ds, lb=1):
dataX, dataY = [], []
for i in range(len(ds)-lb-1):
a = ds[i:(i+lb), 0]
dataX.append(a)
dataY.append(ds[i + lb, 0])
return numpy.array(dataX), numpy.array(dataY)
# fix random seed for reproducibility
numpy.random.seed(7)
# load the dataset
dataframe = df_forecasting
dataset = dataframe.values
dataset = dataset.astype('float32')
# normalize the dataset
scaler = MinMaxScaler(feature_range=(0, 1))
scaler.fit([[0], [50]]) # Maximum expected population is ~50 for problem-related reasons
dataset = scaler.transform(dataset)
# split into train and test sets
train_size = list(df_forecasting.index > pd.to_datetime('20200101')).index(True) # I want to see about forecasting 2020
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], trainX.shape[1], 1))
testX = numpy.reshape(testX, (testX.shape[0], testX.shape[1], 1))
# create and fit the LSTM network
batch_size = 1
model = Sequential()
model.add(LSTM(1, batch_input_shape=(batch_size, look_back, 1), stateful=True, use_bias=False))
model.add(Dense(1, activation='linear', use_bias=False))
model.compile(loss='mean_squared_error', optimizer='adam')
for i in range(1):
model.fit(trainX, trainY, epochs=1, batch_size=batch_size, verbose=2, shuffle=False)
model.reset_states()
# make predictions
trainPredict = model.predict(trainX, batch_size=batch_size)
model.reset_states()
testPredict = model.predict(testX, batch_size=batch_size)
# 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.figure(figsize=(15, 10))
plt.plot(scaler.inverse_transform(dataset), c="g", label="Original Data")
plt.plot(trainPredictPlot, c="b", label="Train Prediction")
plt.plot(testPredictPlot, c="r", label="Test Prediction")
plt.legend()
plt.show()
print(model.summary())
所以这个模型和我想的一样贫乏，无法用于 LSTM，但是，结果如下：
我难住了。我已经跟踪了代码，但与我尝试过的其他模型相比，我根本不明白它是如何工作得这么好的。我的一个理论是这个数据实际上是一个移动平均线，但它是一个因果平均线，所以我看不出这会如何泄露信息。即使可以，9个参数可以使用吗？
很想更好地了解这里发生了什么。这张地图是 17，与我尝试过的其他东西相比，我觉得这很不可思议。当我解开模型（101 个参数，10 个步骤，7 天回溯）时，我将 MAPE 降至 9。我认为如果我允许它会大大降低，但我想先相信......