第81步时间序列建模实战：Adaboost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AdaBoost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、AdaBoost回归

（1）代码解读

sklearn.ensemble.AdaBoostRegressor(estimator=None, *, n_estimators=50, learning_rate=1.0, loss='linear', random_state=None, base_estimator='deprecated')

咋一看，跟AdaBoostClassifier（用于分类，上传送门）参数也差不多，因此，我们列举出它们相同和不同的地方，便于对比记忆：

共同的参数：

base_estimator: 基估计器用于训练弱学习器。如果为 None，分类器默认使用决策树分类器，而回归器默认使用决策树回归器。

n_estimators: 最大的弱学习器数量。

learning_rate: 按指定的学习率缩小每个弱学习器的贡献。

random_state: 随机数生成器的种子或随机数生成器。

algorithm: 用于 AdaBoost 算法的执行版本。在分类器中是 {"SAMME", "SAMME.R"}，在回归器中只有 "SAMME"。

差异：

AdaBoostClassifier 特有参数：

algorithm: 可选的执行算法可以是 "SAMME" 或 "SAMME.R"。默认为 "SAMME.R"。其中 "SAMME.R" 是 "SAMME" 的实值版本，它通常表现得更好，因为它依赖于类别概率，而不是类别预测。

AdaBoostRegressor 特有参数：

loss: 在增加新的弱学习器时用于更新权重的损失函数。可选的值包括 'linear', 'square', 和 'exponential'。

综上可见，虽然这两个类的大部分参数都很相似，但它们的主要区别在于分类器具有两种执行算法（"SAMME" 和 "SAMME.R"），而回归器则添加了一个 loss 参数来定义更新权重时使用的损失函数。

（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 sklearn.ensemble import AdaBoostRegressor
from sklearn.model_selection import GridSearchCV

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')

# 拆分输入和输出
lag_period = 6

# 创建滞后期特征
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']]
y_train = train_data['incidence']
X_validation = validation_data[['lag_1', 'lag_2', 'lag_3', 'lag_4', 'lag_5', 'lag_6']]
y_validation = validation_data['incidence']

# 初始化AdaBoostRegressor模型
adaboost_model = AdaBoostRegressor()

# 定义参数网格
param_grid = {
    'n_estimators': [50, 100, 150],
    'learning_rate': [0.01, 0.05, 0.1, 0.5, 1],
    'loss': ['linear', 'square', 'exponential']
}

# 初始化网格搜索
grid_search = GridSearchCV(adaboost_model, param_grid, cv=5, scoring='neg_mean_squared_error')

# 进行网格搜索
grid_search.fit(X_train, y_train)

# 获取最佳参数
best_params = grid_search.best_params_

# 使用最佳参数初始化AdaBoostRegressor模型
best_adaboost_model = AdaBoostRegressor(**best_params)

# 在训练集上训练模型
best_adaboost_model.fit(X_train, y_train)

# 对于验证集，我们需要迭代地预测每一个数据点
y_validation_pred = []

for i in range(len(X_validation)):
    if i == 0:
        pred = best_adaboost_model.predict([X_validation.iloc[0]])
    else:
        new_features = list(X_validation.iloc[i, 1:]) + [pred[0]]
        pred = best_adaboost_model.predict([new_features])
    y_validation_pred.append(pred[0])

y_validation_pred = np.array(y_validation_pred)

# 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)

# 计算训练集上的MAE, MAPE, MSE和RMSE
y_train_pred = best_adaboost_model.predict(X_train)
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("Train Metrics:", mae_train, mape_train, mse_train, rmse_train)
print("Validation Metrics:", mae_validation, mape_validation, mse_validation, rmse_validation)

看结果：

（3）多步滚动预测-vol. 1

AdaBoostRegressor预期的目标变量y应该是一维数组，所以你们懂的。

（4）多步滚动预测-vol. 2

同上。

（5）多步滚动预测-vol. 3

import pandas as pd
import numpy as np
from sklearn.ensemble import AdaBoostRegressor
from sklearn.model_selection import GridSearchCV
from sklearn.metrics import mean_absolute_error, mean_squared_error

# 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)]
    y_train_list[i] = y_train_list[i].iloc[:len(X_train_list[i])]

# 模型训练
param_grid = {
    'n_estimators': [50, 100, 150],
    'learning_rate': [0.01, 0.05, 0.1, 0.5, 1],
    'loss': ['linear', 'square', 'exponential']
}

best_ada_models = []

for i in range(m):
    grid_search = GridSearchCV(AdaBoostRegressor(), param_grid, cv=5, scoring='neg_mean_squared_error')
    grid_search.fit(X_train_list[i], y_train_list[i])
    best_ada_model = AdaBoostRegressor(**grid_search.best_params_)
    best_ada_model.fit(X_train_list[i], y_train_list[i])
    best_ada_models.append(best_ada_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)]]
y_validation_pred_list = [model.predict(X_validation) for model in best_ada_models]
y_train_pred_list = [model.predict(X_train_list[i]) for i, model in enumerate(best_ada_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]

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

结果：