Tensorflow2.0之时间序列预测

项目介绍

任务：通过前n个时间点的温度来预测第n+1个时间点的温度。
数据集：2009_2016耶拿天气数据集。

Tensorflow实现

1、导入需要的库

import tensorflow as tf

import matplotlib as mpl
import matplotlib.pyplot as plt
import numpy as np
import os
import pandas as pd

mpl.rcParams['figure.figsize'] = (8, 6)
mpl.rcParams['axes.grid'] = False

2、引入数据集

zip_path = tf.keras.utils.get_file(
    origin='https://storage.googleapis.com/tensorflow/tf-keras-datasets/jena_climate_2009_2016.csv.zip',
    fname='jena_climate_2009_2016.csv.zip',
    extract=True)
csv_path, _ = os.path.splitext(zip_path)
df = pd.read_csv(csv_path)
df.head()

输出数据集前五行为：

3、划分特征和标签、建模预测

3.1 用单变量预测一个未来时间点

在这里，我们只是用过去的一些温度信息来预测未来的一个时间点的温度。也就是说，数据集中只包括温度信息。

3.1.1 取出只含温度的数据集

uni_data = df['T (degC)']
uni_data.index = df['Date Time']
uni_data.head()

输出数据集中的前五行：

Date Time
01.01.2009 00:10:00   -8.02
01.01.2009 00:20:00   -8.41
01.01.2009 00:30:00   -8.51
01.01.2009 00:40:00   -8.31
01.01.2009 00:50:00   -8.27
Name: T (degC), dtype: float64

3.1.2 温度随时间变化绘图

uni_data.plot(subplots=True)

3.1.3 将数据集转换为数组类型

uni_data = uni_data.values
uni_data.shape

得到：

(420551,)

可见数据集中包含了420551个时间点的温度信息。

3.1.4 标准化

TRAIN_SPLIT = 300000  # 只取前300000行数据 
uni_train_mean = uni_data[:TRAIN_SPLIT].mean()
uni_train_std = uni_data[:TRAIN_SPLIT].std()
uni_data = (uni_data-uni_train_mean)/uni_train_std

3.1.5 写函数来划分特征和标签

def univariate_data(dataset, start_index, end_index, history_size, target_size):
    data = []
    labels = []

    start_index = start_index + history_size
    if end_index is None:
        end_index = len(dataset) - target_size

    for i in range(start_index, end_index):
        indices = range(i-history_size, i)
        # Reshape data from (history_size,) to (history_size, 1)
        data.append(np.reshape(dataset[indices], (history_size, 1)))
        labels.append(dataset[i+target_size])
    return np.array(data), np.array(labels)

以上函数表示用前history_size个时间点的温度预测第history_size+target_size+1个时间点的温度。start_index和end_index表示数据集datasets起始的时间点，我们将要从这些时间点中取出特征和标签。

3.1.6 从数据集中划分特征和标签

univariate_past_history = 20
univariate_future_target = 0

x_train_uni, y_train_uni = univariate_data(uni_data, 0, TRAIN_SPLIT,
                                           univariate_past_history,
                                           univariate_future_target)
x_val_uni, y_val_uni = univariate_data(uni_data, TRAIN_SPLIT, None,
                                       univariate_past_history,
                                       univariate_future_target)

以上代码说明：每个样本有20个特征（即20个时间点的温度信息），其标签为第21个时间点的温度值，如：

print(uni_data[:25])
print ('Single window of past history')
print (x_train_uni[0])
print ('\n Target temperature to predict')
print (y_train_uni[0])

得到：

array([-1.99766294, -2.04281897, -2.05439744, -2.0312405 , -2.02660912,
       -2.00113649, -1.95134907, -1.95134907, -1.98492663, -2.04513467,
       -2.08334362, -2.09723778, -2.09376424, -2.09144854, -2.07176515,
       -2.07176515, -2.07639653, -2.08913285, -2.09260639, -2.10418486,
       -2.10418486, -2.09492208, -2.10997409, -2.11692118, -2.13776242])
Single window of past history
[[-1.99766294]
 [-2.04281897]
 [-2.05439744]
 [-2.0312405 ]
 [-2.02660912]
 [-2.00113649]
 [-1.95134907]
 [-1.95134907]
 [-1.98492663]
 [-2.04513467]
 [-2.08334362]
 [-2.09723778]
 [-2.09376424]
 [-2.09144854]
 [-2.07176515]
 [-2.07176515]
 [-2.07639653]
 [-2.08913285]
 [-2.09260639]
 [-2.10418486]]

 Target temperature to predict
-2.1041848598100876

可见第一个样本的特征为前20个时间点的温度，其标签为第21个时间点的温度。根据同样的规律，第二个样本的特征为第2个时间点的温度值到第21个时间点的温度值，其标签为第22个时间点的温度……

3.1.7 设置绘图函数

def create_time_steps(length):
    return list(range(-length, 0))
def show_plot(plot_data, delta, title):
    labels = ['History', 'True Future', 'Model Prediction']
    marker = ['.-', 'rx', 'go']
    time_steps = create_time_steps(plot_data[0].shape[0])  # 返回-20到-1的列表
    if delta:
        future = delta
    else:
        future = 0

    plt.title(title)
    for i, x in enumerate(plot_data):
        if i:
            plt.plot(future, plot_data[i], marker[i], markersize=10,
                     label=labels[i])
        else:
            plt.plot(time_steps, plot_data[i].flatten(), marker[i], label=labels[i])
    plt.legend()
    plt.xlim([time_steps[0], (future+5)*2])
    plt.xlabel('Time-Step')
    return plt

以上代码中的create_time_steps(length) 函数即创造一个从-20到-1的列表，作为x轴的数值。

3.1.8 绘制第一个样本的特征和标签

因为此时还没有预测值，所以绘图函数中的’Model Prediction’是用不到的。

show_plot([x_train_uni[0], y_train_uni[0]], 0, 'Sample Example')

3.1.9 将特征和标签切片

BATCH_SIZE = 256
BUFFER_SIZE = 10000

train_univariate = tf.data.Dataset.from_tensor_slices((x_train_uni, y_train_uni))
train_univariate = train_univariate.cache().shuffle(BUFFER_SIZE).batch(BATCH_SIZE).repeat()

val_univariate = tf.data.Dataset.from_tensor_slices((x_val_uni, y_val_uni))
val_univariate = val_univariate.batch(BATCH_SIZE).repeat()

我们可以通过：

for x, y in val_univariate.take(1):
    print(x.shape)
    print(y.shape)

来查看每批样本的尺寸。

(256, 20, 1)
(256,)

3.1.10 建模

simple_lstm_model = tf.keras.models.Sequential([
    tf.keras.layers.LSTM(8, input_shape=x_train_uni.shape[-2:]),
    tf.keras.layers.Dense(1)
])

simple_lstm_model.compile(optimizer='adam', loss='mae')

3.1.11 训练模型

EVALUATION_INTERVAL = 200
EPOCHS = 10

simple_lstm_model.fit(train_univariate, epochs=EPOCHS,
                      steps_per_epoch=EVALUATION_INTERVAL,
                      validation_data=val_univariate, validation_steps=50)

Train for 200 steps, validate for 50 steps
Epoch 1/10
200/200 [==============================] - 5s 25ms/step - loss: 0.4075 - val_loss: 0.1351
Epoch 2/10
200/200 [==============================] - 2s 10ms/step - loss: 0.1118 - val_loss: 0.0359
Epoch 3/10
200/200 [==============================] - 2s 10ms/step - loss: 0.0489 - val_loss: 0.0290
Epoch 4/10
200/200 [==============================] - 2s 10ms/step - loss: 0.0443 - val_loss: 0.0258
Epoch 5/10
200/200 [==============================] - 2s 10ms/step - loss: 0.0299 - val_loss: 0.0235
Epoch 6/10
200/200 [==============================] - 2s 10ms/step - loss: 0.0317 - val_loss: 0.0224
Epoch 7/10
200/200 [==============================] - 2s 11ms/step - loss: 0.0286 - val_loss: 0.0207
Epoch 8/10
200/200 [==============================] - 2s 11ms/step - loss: 0.0263 - val_loss: 0.0197
Epoch 9/10
200/200 [==============================] - 2s 10ms/step - loss: 0.0253 - val_loss: 0.0181
Epoch 10/10
200/200 [==============================] - 2s 11ms/step - loss: 0.0227 - val_loss: 0.0174

3.1.12 将预测值也绘制在图上

for x, y in val_univariate.take(3):
    plot = show_plot([x[0].numpy(), y[0].numpy(),
                    simple_lstm_model.predict(x)[0]], 0, 'Simple LSTM model')
    plot.show()

3.2 用多变量预测一个未来时间点

在这里，我们用过去的一些压强信息、温度信息以及密度信息来预测未来的一个时间点的温度。也就是说，数据集中应该包括压强信息、温度信息以及密度信息。

3.2.1 取出含所考虑变量的数据集

features_considered = ['p (mbar)', 'T (degC)', 'rho (g/m**3)']
features = df[features_considered]
features.index = df['Date Time']
features.head()

数据集前五行数据为：

3.2.2 压强、温度、密度随时间变化绘图

features.plot(subplots=True)

3.2.3 将数据集转换为数组类型并标准化

dataset = features.values
data_mean = dataset[:TRAIN_SPLIT].mean(axis=0)
data_std = dataset[:TRAIN_SPLIT].std(axis=0)

dataset = (dataset-data_mean)/data_std

3.2.4 写函数来划分特征和标签

在这里，我们不再像3.1中一样用到每个数据，而是在函数中加入step参数，这表明所使用的样本每step个时间点取一次特征和标签。

def multivariate_data(dataset, target, start_index, end_index, history_size,
                      target_size, step, single_step=False):
    data = []
    labels = []

    start_index = start_index + history_size
    if end_index is None:
        end_index = len(dataset) - target_size

    for i in range(start_index, end_index):
        indices = range(i-history_size, i, step)
        data.append(dataset[indices])

        if single_step:
            labels.append(target[i+target_size])
        else:
            labels.append(target[i:i+target_size])

    return np.array(data), np.array(labels)

3.2.5 从数据集中划分特征和标签

past_history = 720
future_target = 72
STEP = 6

x_train_single, y_train_single = multivariate_data(dataset, dataset[:, 1], 0,
                                                   TRAIN_SPLIT, past_history,
                                                   future_target, STEP,
                                                   single_step=True)
x_val_single, y_val_single = multivariate_data(dataset, dataset[:, 1],
                                               TRAIN_SPLIT, None, past_history,
                                               future_target, STEP,
                                               single_step=True)

以上代码说明：每个样本的特征为过去的720个时间点的信息，但由于step被设置为6，则在过去的720个时间点的信息中，有720/6=120个时间点的信息被纳入样本特征。
我们可以打印出样本的特征信息：

print ('Single window of past history : {}'.format(x_train_single[0].shape))

得到单个样本的特征尺寸为：

Single window of past history : (120, 3)

3.2.6 将特征和标签切片

train_data_single = tf.data.Dataset.from_tensor_slices((x_train_single, y_train_single))
train_data_single = train_data_single.cache().shuffle(BUFFER_SIZE).batch(BATCH_SIZE).repeat()

val_data_single = tf.data.Dataset.from_tensor_slices((x_val_single, y_val_single))
val_data_single = val_data_single.batch(BATCH_SIZE).repeat()

3.2.7 建模

single_step_model = tf.keras.models.Sequential()
single_step_model.add(tf.keras.layers.LSTM(32,
                                           input_shape=x_train_single.shape[-2:]))
single_step_model.add(tf.keras.layers.Dense(1))

single_step_model.compile(optimizer=tf.keras.optimizers.RMSprop(), loss='mae')

3.2.8 训练模型

single_step_history = single_step_model.fit(train_data_single, epochs=EPOCHS,
                                            steps_per_epoch=EVALUATION_INTERVAL,
                                            validation_data=val_data_single,
                                            validation_steps=50)

Train for 200 steps, validate for 50 steps
Epoch 1/10
200/200 [==============================] - 35s 176ms/step - loss: 0.3090 - val_loss: 0.2647
Epoch 2/10
200/200 [==============================] - 41s 203ms/step - loss: 0.2625 - val_loss: 0.2432
Epoch 3/10
200/200 [==============================] - 51s 256ms/step - loss: 0.2614 - val_loss: 0.2476
Epoch 4/10
200/200 [==============================] - 61s 307ms/step - loss: 0.2566 - val_loss: 0.2447
Epoch 5/10
200/200 [==============================] - 72s 361ms/step - loss: 0.2267 - val_loss: 0.2360
Epoch 6/10
200/200 [==============================] - 86s 432ms/step - loss: 0.2413 - val_loss: 0.2667
Epoch 7/10
200/200 [==============================] - 82s 412ms/step - loss: 0.2414 - val_loss: 0.2577
Epoch 8/10
200/200 [==============================] - 76s 378ms/step - loss: 0.2407 - val_loss: 0.2371
Epoch 9/10
200/200 [==============================] - 73s 365ms/step - loss: 0.2447 - val_loss: 0.2486
Epoch 10/10
200/200 [==============================] - 74s 368ms/step - loss: 0.2385 - val_loss: 0.2445

3.2.9 绘制预测图

for x, y in val_data_single.take(3):
    plot = show_plot([x[0][:, 1].numpy(), y[0].numpy(),
                    single_step_model.predict(x)[0]], 12,
                   'Single Step Prediction')
    plot.show()

3.3 用多变量预测多个未来时间点

在这里，我们用过去的一些压强信息、温度信息以及密度信息来预测未来的多个时间点的温度。也就是说，数据集中应该包括压强信息、温度信息以及密度信息。

3.3.1 从数据集中划分特征和标签

future_target = 72
x_train_multi, y_train_multi = multivariate_data(dataset, dataset[:, 1], 0,
                                                 TRAIN_SPLIT, past_history,
                                                 future_target, STEP)
x_val_multi, y_val_multi = multivariate_data(dataset, dataset[:, 1],
                                             TRAIN_SPLIT, None, past_history,
                                             future_target, STEP)

以上代码说明特征的划分方式和3.2中的相同，但每个样本的标签中都包含了未来72个时间点的温度信息。
我们可以打印出样本的特征信息：

print ('Single window of past history : {}'.format(x_train_multi[0].shape))
print ('\n Target temperature to predict : {}'.format(y_train_multi[0].shape))

得到单个样本的特征尺寸为：

Single window of past history : (120, 3)

 Target temperature to predict : (72,)

3.3.2 将特征和标签切片

train_data_multi = tf.data.Dataset.from_tensor_slices((x_train_multi, y_train_multi))
train_data_multi = train_data_multi.cache().shuffle(BUFFER_SIZE).batch(BATCH_SIZE).repeat()

val_data_multi = tf.data.Dataset.from_tensor_slices((x_val_multi, y_val_multi))
val_data_multi = val_data_multi.batch(BATCH_SIZE).repeat()

3.3.3 编写绘图函数

def multi_step_plot(history, true_future, prediction):
    plt.figure(figsize=(12, 6))
    num_in = create_time_steps(len(history))
    num_out = len(true_future)

    plt.plot(num_in, np.array(history[:, 1]), label='History')
    plt.plot(np.arange(num_out)/STEP, np.array(true_future), 'bo',
           label='True Future')
    if prediction.any():
        plt.plot(np.arange(num_out)/STEP, np.array(prediction), 'ro',
                 label='Predicted Future')
    plt.legend(loc='upper left')
    plt.show()

3.3.4 绘制温度信息（不含预测值）

for x, y in train_data_multi.take(1):
    multi_step_plot(x[0], y[0], np.array([0]))

3.3.5 建模

multi_step_model = tf.keras.models.Sequential()
multi_step_model.add(tf.keras.layers.LSTM(32,
                                          return_sequences=True,
                                          input_shape=x_train_multi.shape[-2:]))
multi_step_model.add(tf.keras.layers.LSTM(16, activation='relu'))
multi_step_model.add(tf.keras.layers.Dense(72))

multi_step_model.compile(optimizer=tf.keras.optimizers.RMSprop(clipvalue=1.0), loss='mae')

3.3.6 训练模型

multi_step_history = multi_step_model.fit(train_data_multi, epochs=EPOCHS,
                                          steps_per_epoch=EVALUATION_INTERVAL,
                                          validation_data=val_data_multi,
                                          validation_steps=50)

Train for 200 steps, validate for 50 steps
Epoch 1/10
200/200 [==============================] - 113s 565ms/step - loss: 0.4974 - val_loss: 0.3019
Epoch 2/10
200/200 [==============================] - 119s 593ms/step - loss: 0.3480 - val_loss: 0.2845
Epoch 3/10
200/200 [==============================] - 134s 670ms/step - loss: 0.3335 - val_loss: 0.2523
Epoch 4/10
200/200 [==============================] - 177s 887ms/step - loss: 0.2438 - val_loss: 0.2093
Epoch 5/10
200/200 [==============================] - 167s 837ms/step - loss: 0.1962 - val_loss: 0.2025
Epoch 6/10
200/200 [==============================] - 174s 871ms/step - loss: 0.2062 - val_loss: 0.2108
Epoch 7/10
200/200 [==============================] - 175s 873ms/step - loss: 0.1981 - val_loss: 0.2047
Epoch 8/10
200/200 [==============================] - 169s 846ms/step - loss: 0.1965 - val_loss: 0.1983
Epoch 9/10
200/200 [==============================] - 170s 849ms/step - loss: 0.2001 - val_loss: 0.1873
Epoch 10/10
200/200 [==============================] - 172s 861ms/step - loss: 0.1913 - val_loss: 0.1828

3.3.7 绘制温度信息（含预测值）

for x, y in val_data_multi.take(3):
    multi_step_plot(x[0], y[0], multi_step_model.predict(x)[0])