第86步时间序列建模实战：Transformer回归建模

基于WIN10的64位系统演示

一、写在前面

这一期，我们介绍Transformer回归。

同样，这里使用这个数据：

《PLoS One》2015年一篇题目为《Comparison of Two Hybrid Models for Forecasting the Incidence of Hemorrhagic Fever with Renal Syndrome in Jiangsu Province, China》文章的公开数据做演示。数据为江苏省2004年1月至2012年12月肾综合症出血热月发病率。运用2004年1月至2011年12月的数据预测2012年12个月的发病率数据。

二、Transformer回归

（1）原理

Transformer框架原本是为NLP任务，特别是机器翻译而设计的。但由于其独特的自注意力机制，Transformer在处理顺序数据时表现出色，因此被广泛应用于各种序列数据任务，包括回归任务。

（a）回归任务中的Transformer：

（a1）在回归任务中，Transformer可以捕捉数据中的长期依赖关系。例如，在时间序列数据中，Transformer可以捕捉时间点之间的关系，即使这些时间点相隔很远。

（a2）为回归任务使用Transformer时，通常需要稍微调整模型结构，特别是模型的输出部分。原始的Transformer用于生成序列，但在回归任务中，我们通常需要一个单一的实数作为输出。

（b）Transformer的优点：

（b1）自注意力机制：可以捕捉序列中的任意位置间的依赖关系，而不像RNN那样依赖于前面的信息。

（b2）并行计算：与RNN或LSTM不同，Transformer不需要按顺序处理数据，因此更容易并行处理，提高训练速度。

（b3）可扩展性：可以通过堆叠多个Transformer层来捕捉复杂的模式和关系。

模型解释性：由于自注意力机制，我们可以可视化哪些输入位置对于特定输出最为重要，这增加了模型的解释性。

（c）Transformer的缺点：

（c1）计算需求：尽管可以并行化，但Transformer模型，特别是大型模型，仍然需要大量的计算资源。

（c2）过拟合：在小型数据集上，特别是没有足够的正则化时，Transformer可能会过拟合。

（c3）长序列的挑战：尽管Transformer可以处理长序列，但由于自注意力机制的复杂性，处理非常长的序列仍然是一个挑战。为此，研究人员已经提出了许多变种，例如Reformer。

总体而言，Transformer提供了一个强大的框架来处理各种序列数据任务。

（2）单步滚动预测

import pandas as pd
import numpy as np
from sklearn.metrics import mean_absolute_error, mean_squared_error
from tensorflow.python.keras.models import Sequential
from tensorflow.python.keras import layers, models, optimizers
from tensorflow.python.keras.optimizers import adam_v2

# 读取数据
data = pd.read_csv('data.csv')

# 将时间列转换为日期格式
data['time'] = pd.to_datetime(data['time'], format='%b-%y')

# 创建滞后期特征
lag_period = 6
for i in range(lag_period, 0, -1):
    data[f'lag_{i}'] = data['incidence'].shift(lag_period - i + 1)

# 删除包含 NaN 的行
data = data.dropna().reset_index(drop=True)

# 划分训练集和验证集
train_data = data[(data['time'] >= '2004-01-01') & (data['time'] <= '2011-12-31')]
validation_data = data[(data['time'] >= '2012-01-01') & (data['time'] <= '2012-12-31')]

# 定义特征和目标变量
X_train = train_data[['lag_1', 'lag_2', 'lag_3', 'lag_4', 'lag_5', 'lag_6']].values
y_train = train_data['incidence'].values
X_validation = validation_data[['lag_1', 'lag_2', 'lag_3', 'lag_4', 'lag_5', 'lag_6']].values
y_validation = validation_data['incidence'].values

# 对于Transformer，我们需要将输入数据重塑为 [samples, timesteps, features]
X_train = X_train.reshape(X_train.shape[0], X_train.shape[1], 1)
X_validation = X_validation.reshape(X_validation.shape[0], X_validation.shape[1], 1)

# Transformer的一些参数设置
d_model = 128
num_heads = 4

# 构建Transformer回归模型
input_layer = layers.Input(shape=(X_train.shape[1], 1))

# Linear Embedding
x = layers.Dense(d_model)(input_layer)

# Multi Head Self Attention
x = layers.MultiHeadAttention(num_heads=num_heads, key_dim=d_model)(x, x)

# Feed Forward Neural Networks
x = layers.GlobalAveragePooling1D()(x)
x = layers.Dropout(0.1)(x)
x = layers.Dense(50, activation='relu')(x)
x = layers.Dropout(0.1)(x)
output_layer = layers.Dense(1)(x)

model = models.Model(inputs=input_layer, outputs=output_layer)

model.compile(optimizer=adam_v2.Adam(learning_rate=0.001), loss='mse')

# 训练模型
history = model.fit(X_train, y_train, epochs=200, batch_size=32, validation_data=(X_validation, y_validation), verbose=0)

# 单步滚动预测函数
def rolling_forecast(model, initial_features, n_forecasts):
    forecasts = []
    current_features = initial_features.copy()

    for i in range(n_forecasts):
        # 使用当前的特征进行预测
        forecast = model.predict(current_features.reshape(1, len(current_features), 1)).flatten()[0]
        forecasts.append(forecast)

        # 更新特征，用新的预测值替换最旧的特征
        current_features = np.roll(current_features, shift=-1)
        current_features[-1] = forecast

    return np.array(forecasts)

# 使用训练集的最后6个数据点作为初始特征
initial_features = X_train[-1].flatten()

# 使用单步滚动预测方法预测验证集
y_validation_pred = rolling_forecast(model, initial_features, len(X_validation))

# 计算训练集上的MAE, MAPE, MSE 和 RMSE
mae_train = mean_absolute_error(y_train, model.predict(X_train).flatten())
mape_train = np.mean(np.abs((y_train - model.predict(X_train).flatten()) / y_train))
mse_train = mean_squared_error(y_train, model.predict(X_train).flatten())
rmse_train = np.sqrt(mse_train)

# 计算验证集上的MAE, MAPE, MSE 和 RMSE
mae_validation = mean_absolute_error(y_validation, y_validation_pred)
mape_validation = np.mean(np.abs((y_validation - y_validation_pred) / y_validation))
mse_validation = mean_squared_error(y_validation, y_validation_pred)
rmse_validation = np.sqrt(mse_validation)

print("验证集：", mae_validation, mape_validation, mse_validation, rmse_validation)
print("训练集：", mae_train, mape_train, mse_train, rmse_train)

看结果：

（3）多步滚动预测-vol. 1

import pandas as pd
import numpy as np
from sklearn.metrics import mean_absolute_error, mean_squared_error
import tensorflow as tf
from tensorflow.python.keras.models import Model
from tensorflow.python.keras.layers import Input, MultiHeadAttention, Dense, Dropout, LayerNormalization, Flatten
from tensorflow.python.keras.optimizers import adam_v2

# 读取数据
data = pd.read_csv('data.csv')
data['time'] = pd.to_datetime(data['time'], format='%b-%y')

n = 6
m = 2

# 创建滞后期特征
for i in range(n, 0, -1):
    data[f'lag_{i}'] = data['incidence'].shift(n - i + 1)

data = data.dropna().reset_index(drop=True)

train_data = data[(data['time'] >= '2004-01-01') & (data['time'] <= '2011-12-31')]
validation_data = data[(data['time'] >= '2012-01-01') & (data['time'] <= '2012-12-31')]

# 准备训练数据
X_train = []
y_train = []

for i in range(len(train_data) - n - m + 1):
    X_train.append(train_data.iloc[i+n-1][[f'lag_{j}' for j in range(1, n+1)]].values)
    y_train.append(train_data.iloc[i+n:i+n+m]['incidence'].values)

X_train = np.array(X_train)
y_train = np.array(y_train)
X_train = X_train.astype(np.float32)
y_train = y_train.astype(np.float32)

# 构建Transformer模型
inputs = Input(shape=(n, 1))

x = MultiHeadAttention(num_heads=8, key_dim=64)(inputs, inputs)
x = Dropout(0.1)(x)
x = LayerNormalization(epsilon=1e-6)(x + inputs)

x = Flatten()(x) # 新增的Flatten层
x = Dense(50, activation='relu')(x)
x = Dropout(0.1)(x)
outputs = Dense(m)(x)

model = Model(inputs=inputs, outputs=outputs)

model.compile(optimizer=adam_v2.Adam(learning_rate=0.001), loss='mse')

# 训练模型
model.fit(X_train, y_train, epochs=200, batch_size=32, verbose=0)

def transformer_rolling_forecast(data, model, n, m):
    y_pred = []

    for i in range(len(data) - n):
        input_data = data.iloc[i+n-1][[f'lag_{j}' for j in range(1, n+1)]].values.astype(np.float32).reshape(1, n, 1)
        pred = model.predict(input_data)
        y_pred.extend(pred[0])

    for i in range(1, m):
        for j in range(len(y_pred) - i):
            y_pred[j+i] = (y_pred[j+i] + y_pred[j]) / 2

    return np.array(y_pred)

# Predict for train_data and validation_data
y_train_pred_transformer = transformer_rolling_forecast(train_data, model, n, m)[:len(y_train)]
y_validation_pred_transformer = transformer_rolling_forecast(validation_data, model, n, m)[:len(validation_data) - n]

# Calculate performance metrics for train_data
mae_train = mean_absolute_error(train_data['incidence'].values[n:len(y_train_pred_transformer)+n], y_train_pred_transformer)
mape_train = np.mean(np.abs((train_data['incidence'].values[n:len(y_train_pred_transformer)+n] - y_train_pred_transformer) / train_data['incidence'].values[n:len(y_train_pred_transformer)+n]))
mse_train = mean_squared_error(train_data['incidence'].values[n:len(y_train_pred_transformer)+n], y_train_pred_transformer)
rmse_train = np.sqrt(mse_train)

# Calculate performance metrics for validation_data
mae_validation = mean_absolute_error(validation_data['incidence'].values[n:len(y_validation_pred_transformer)+n], y_validation_pred_transformer)
mape_validation = np.mean(np.abs((validation_data['incidence'].values[n:len(y_validation_pred_transformer)+n] - y_validation_pred_transformer) / validation_data['incidence'].values[n:len(y_validation_pred_transformer)+n]))
mse_validation = mean_squared_error(validation_data['incidence'].values[n:len(y_validation_pred_transformer)+n], y_validation_pred_transformer)
rmse_validation = np.sqrt(mse_validation)

print("训练集：", mae_train, mape_train, mse_train, rmse_train)
print("验证集：", mae_validation, mape_validation, mse_validation, rmse_validation)

结果：

（4）多步滚动预测-vol. 2

import pandas as pd
import numpy as np
from sklearn.model_selection import train_test_split
from sklearn.metrics import mean_absolute_error, mean_squared_error
from tensorflow.python.keras.models import Sequential, Model
from tensorflow.python.keras.layers import Dense, Conv1D, Flatten, MaxPooling1D, Input, MultiHeadAttention, LayerNormalization, Dropout
from tensorflow.python.keras.optimizers import adam_v2

# Loading and preprocessing the data
data = pd.read_csv('data.csv')
data['time'] = pd.to_datetime(data['time'], format='%b-%y')

n = 6
m = 2

# 创建滞后期特征
for i in range(n, 0, -1):
    data[f'lag_{i}'] = data['incidence'].shift(n - i + 1)

data = data.dropna().reset_index(drop=True)

train_data = data[(data['time'] >= '2004-01-01') & (data['time'] <= '2011-12-31')]
validation_data = data[(data['time'] >= '2012-01-01') & (data['time'] <= '2012-12-31')]

# 只对X_train、y_train、X_validation取奇数行
X_train = train_data[[f'lag_{i}' for i in range(1, n+1)]].iloc[::2].reset_index(drop=True).values
X_train = X_train.reshape(X_train.shape[0], X_train.shape[1], 1)

y_train_list = [train_data['incidence'].shift(-i) for i in range(m)]
y_train = pd.concat(y_train_list, axis=1)
y_train.columns = [f'target_{i+1}' for i in range(m)]
y_train = y_train.iloc[::2].reset_index(drop=True).dropna().values[:, 0]

X_validation = validation_data[[f'lag_{i}' for i in range(1, n+1)]].iloc[::2].reset_index(drop=True).values
X_validation = X_validation.reshape(X_validation.shape[0], X_validation.shape[1], 1)

y_validation = validation_data['incidence'].values

# Building the Transformer model
inputs = Input(shape=(n, 1))
x = MultiHeadAttention(num_heads=8, key_dim=64)(inputs, inputs)
x = Dropout(0.1)(x)
x = LayerNormalization(epsilon=1e-6)(x + inputs)
x = Flatten()(x)
x = Dense(50, activation='relu')(x)
outputs = Dense(1)(x)

model = Model(inputs=inputs, outputs=outputs)
optimizer = adam_v2.Adam(learning_rate=0.001)
model.compile(optimizer=optimizer, loss='mse')

# Train the model
model.fit(X_train, y_train, epochs=200, batch_size=32, verbose=0)

# Predict on validation set
y_validation_pred = model.predict(X_validation).flatten()

# Compute metrics for validation set
mae_validation = mean_absolute_error(y_validation[:len(y_validation_pred)], y_validation_pred)
mape_validation = np.mean(np.abs((y_validation[:len(y_validation_pred)] - y_validation_pred) / y_validation[:len(y_validation_pred)]))
mse_validation = mean_squared_error(y_validation[:len(y_validation_pred)], y_validation_pred)
rmse_validation = np.sqrt(mse_validation)

# Predict on training set
y_train_pred = model.predict(X_train).flatten()

# Compute metrics for training set
mae_train = mean_absolute_error(y_train, y_train_pred)
mape_train = np.mean(np.abs((y_train - y_train_pred) / y_train))
mse_train = mean_squared_error(y_train, y_train_pred)
rmse_train = np.sqrt(mse_train)

print("验证集：", mae_validation, mape_validation, mse_validation, rmse_validation)
print("训练集：", mae_train, mape_train, mse_train, rmse_train)

结果：

（5）多步滚动预测-vol. 3

import pandas as pd
import numpy as np
from sklearn.metrics import mean_absolute_error, mean_squared_error
from tensorflow.python.keras.models import Sequential, Model
from tensorflow.python.keras.layers import Dense, Flatten, Input, MultiHeadAttention, LayerNormalization, Dropout
from tensorflow.python.keras.optimizers import adam_v2

# 数据读取和预处理
data = pd.read_csv('data.csv')
data_y = pd.read_csv('data.csv')
data['time'] = pd.to_datetime(data['time'], format='%b-%y')
data_y['time'] = pd.to_datetime(data_y['time'], format='%b-%y')

n = 6

for i in range(n, 0, -1):
    data[f'lag_{i}'] = data['incidence'].shift(n - i + 1)

data = data.dropna().reset_index(drop=True)
train_data = data[(data['time'] >= '2004-01-01') & (data['time'] <= '2011-12-31')]
X_train = train_data[[f'lag_{i}' for i in range(1, n+1)]]
m = 3

X_train_list = []
y_train_list = []

for i in range(m):
    X_temp = X_train
    y_temp = data_y['incidence'].iloc[n + i:len(data_y) - m + 1 + i]
    
    X_train_list.append(X_temp)
    y_train_list.append(y_temp)

for i in range(m):
    X_train_list[i] = X_train_list[i].iloc[:-(m-1)].values
    X_train_list[i] = X_train_list[i].reshape(X_train_list[i].shape[0], X_train_list[i].shape[1], 1)
    y_train_list[i] = y_train_list[i].iloc[:len(X_train_list[i])].values

# 模型训练
models = []
for i in range(m):
    # Building the Transformer model
    inputs = Input(shape=(n, 1))
    x = MultiHeadAttention(num_heads=8, key_dim=64)(inputs, inputs)
    x = Dropout(0.1)(x)
    x = LayerNormalization(epsilon=1e-6)(x + inputs)
    x = Flatten()(x)
    x = Dense(50, activation='relu')(x)
    outputs = Dense(1)(x)

    model = Model(inputs=inputs, outputs=outputs)
    optimizer = adam_v2.Adam(learning_rate=0.001)
    model.compile(optimizer=optimizer, loss='mse')
    model.fit(X_train_list[i], y_train_list[i], epochs=200, batch_size=32, verbose=0)
    models.append(model)

validation_start_time = train_data['time'].iloc[-1] + pd.DateOffset(months=1)
validation_data = data[data['time'] >= validation_start_time]
X_validation = validation_data[[f'lag_{i}' for i in range(1, n+1)]].values
X_validation = X_validation.reshape(X_validation.shape[0], X_validation.shape[1], 1)

y_validation_pred_list = [model.predict(X_validation) for model in models]
y_train_pred_list = [model.predict(X_train_list[i]) for i, model in enumerate(models)]

def concatenate_predictions(pred_list):
    concatenated = []
    for j in range(len(pred_list[0])):
        for i in range(m):
            concatenated.append(pred_list[i][j])
    return concatenated

y_validation_pred = np.array(concatenate_predictions(y_validation_pred_list))[:len(validation_data['incidence'])]
y_train_pred = np.array(concatenate_predictions(y_train_pred_list))[:len(train_data['incidence']) - m + 1]
y_validation_pred = y_validation_pred.flatten()
y_train_pred = y_train_pred.flatten()

mae_validation = mean_absolute_error(validation_data['incidence'], y_validation_pred)
mape_validation = np.mean(np.abs((validation_data['incidence'] - y_validation_pred) / validation_data['incidence']))
mse_validation = mean_squared_error(validation_data['incidence'], y_validation_pred)
rmse_validation = np.sqrt(mse_validation)

mae_train = mean_absolute_error(train_data['incidence'][:-(m-1)], y_train_pred)
mape_train = np.mean(np.abs((train_data['incidence'][:-(m-1)] - y_train_pred) / train_data['incidence'][:-(m-1)]))
mse_train = mean_squared_error(train_data['incidence'][:-(m-1)], y_train_pred)
rmse_train = np.sqrt(mse_train)

print("验证集：", mae_validation, mape_validation, mse_validation, rmse_validation)
print("训练集：", mae_train, mape_train, mse_train, rmse_train)

结果：