• 第87步 时间序列建模实战：LSTM回归建模

    基于WIN10的64位系统演示

    一、写在前面

    这一期，我们介绍大名鼎鼎的LSTM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、LSTM回归

    （1）LSTM简介

    LSTM (Long Short-Term Memory) 是一种特殊的RNN（递归神经网络）结构，由Hochreiter和Schmidhuber在1997年首次提出。LSTM 被设计出来是为了避免长序列在训练过程中的长期依赖问题，这是传统 RNNs 所普遍遇到问题。

    （a）LSTM 的主要特点：

    （a1）三个门结构：LSTM 包含三个门结构：输入门、遗忘门和输出门。这些门决定了信息如何进入、被存储或被遗忘，以及如何输出。

    （a2）记忆细胞：LSTM的核心是称为记忆细胞的结构。它可以保留、修改或访问的内部状态。通过门结构，模型可以学会在记忆细胞中何时存储、忘记或检索信息。

    （a3）长期依赖问题：LSTM特别擅长学习、存储和使用长期信息，从而避免了传统RNN在长序列上的梯度消失问题。

    （b）为什么LSTM适合时间序列建模：

    （b1）序列数据的特性：时间序列数据具有顺序性，先前的数据点可能会影响后面的数据点。LSTM设计之初就是为了处理带有时间间隔、延迟和长期依赖关系的序列数据。

    （b2）长期依赖：在时间序列分析中，某个事件可能会受到很早之前事件的影响。传统的RNNs由于梯度消失的问题，很难捕捉这些长期依赖关系。但是，LSTM结构可以有效地处理这种依赖关系。

    （b3）记忆细胞：对于时间序列预测，能够记住过去的信息是至关重要的。LSTM的记忆细胞可以为模型提供这种存储和检索长期信息的能力。

    （b4）灵活性：LSTM模型可以与其他神经网络结构（如CNN）结合，用于更复杂的时间序列任务，例如多变量时间序列或序列生成。

    综上所述，由于LSTM的设计和特性，它非常适合时间序列建模，尤其是当数据具有长期依赖关系时。

    （2）单步滚动预测

    1. import pandas as pd
    2. import numpy as np
    3. from sklearn.metrics import mean_absolute_error, mean_squared_error
    4. from tensorflow.python.keras.models import Sequential
    5. from tensorflow.python.keras import layers, models, optimizers
    6. from tensorflow.python.keras.optimizers import adam_v2
    7.  
    8. # 读取数据
    9. data = pd.read_csv('data.csv')
    10.  
    11. # 将时间列转换为日期格式
    12. data['time'] = pd.to_datetime(data['time'], format='%b-%y')
    13.  
    14. # 创建滞后期特征
    15. lag_period = 6
    16. for i in range(lag_period, 0, -1):
    17.     data[f'lag_{i}'] = data['incidence'].shift(lag_period - i + 1)
    18.  
    19. # 删除包含 NaN 的行
    20. data = data.dropna().reset_index(drop=True)
    21.  
    22. # 划分训练集和验证集
    23. train_data = data[(data['time'] >= '2004-01-01') & (data['time'] <= '2011-12-31')]
    24. validation_data = data[(data['time'] >= '2012-01-01') & (data['time'] <= '2012-12-31')]
    25.  
    26. # 定义特征和目标变量
    27. X_train = train_data[['lag_1', 'lag_2', 'lag_3', 'lag_4', 'lag_5', 'lag_6']].values
    28. y_train = train_data['incidence'].values
    29. X_validation = validation_data[['lag_1', 'lag_2', 'lag_3', 'lag_4', 'lag_5', 'lag_6']].values
    30. y_validation = validation_data['incidence'].values
    31.  
    32. # 对于LSTM，我们需要将输入数据重塑为 [samples, timesteps, features]
    33. X_train = X_train.reshape(X_train.shape[0], X_train.shape[1], 1)
    34. X_validation = X_validation.reshape(X_validation.shape[0], X_validation.shape[1], 1)
    35.  
    36. # 构建LSTM回归模型
    37. input_layer = layers.Input(shape=(X_train.shape[1], 1))
    38.  
    39. x = layers.LSTM(50, return_sequences=True)(input_layer)
    40. x = layers.LSTM(25, return_sequences=False)(x)
    41. x = layers.Dropout(0.1)(x)
    42. x = layers.Dense(25, activation='relu')(x)
    43. x = layers.Dropout(0.1)(x)
    44. output_layer = layers.Dense(1)(x)
    45.  
    46. model = models.Model(inputs=input_layer, outputs=output_layer)
    47.  
    48. model.compile(optimizer=adam_v2.Adam(learning_rate=0.001), loss='mse')
    49.  
    50. # 训练模型
    51. history = model.fit(X_train, y_train, epochs=200, batch_size=32, validation_data=(X_validation, y_validation), verbose=0)
    52.  
    53. # 单步滚动预测函数
    54. def rolling_forecast(model, initial_features, n_forecasts):
    55.     forecasts = []
    56.     current_features = initial_features.copy()
    57.  
    58.     for i in range(n_forecasts):
    59.         # 使用当前的特征进行预测
    60.         forecast = model.predict(current_features.reshape(1, len(current_features), 1)).flatten()[0]
    61.         forecasts.append(forecast)
    62.  
    63.         # 更新特征，用新的预测值替换最旧的特征
    64.         current_features = np.roll(current_features, shift=-1)
    65.         current_features[-1] = forecast
    66.  
    67.     return np.array(forecasts)
    68.  
    69. # 使用训练集的最后6个数据点作为初始特征
    70. initial_features = X_train[-1].flatten()
    71.  
    72. # 使用单步滚动预测方法预测验证集
    73. y_validation_pred = rolling_forecast(model, initial_features, len(X_validation))
    74.  
    75. # 计算训练集上的MAE, MAPE, MSE 和 RMSE
    76. mae_train = mean_absolute_error(y_train, model.predict(X_train).flatten())
    77. mape_train = np.mean(np.abs((y_train - model.predict(X_train).flatten()) / y_train))
    78. mse_train = mean_squared_error(y_train, model.predict(X_train).flatten())
    79. rmse_train = np.sqrt(mse_train)
    80.  
    81. # 计算验证集上的MAE, MAPE, MSE 和 RMSE
    82. mae_validation = mean_absolute_error(y_validation, y_validation_pred)
    83. mape_validation = np.mean(np.abs((y_validation - y_validation_pred) / y_validation))
    84. mse_validation = mean_squared_error(y_validation, y_validation_pred)
    85. rmse_validation = np.sqrt(mse_validation)
    86.  
    87. print("验证集：", mae_validation, mape_validation, mse_validation, rmse_validation)
    88. print("训练集：", mae_train, mape_train, mse_train, rmse_train)

    看结果：

    （3）多步滚动预测-vol. 1

    1. import pandas as pd
    2. import numpy as np
    3. from sklearn.metrics import mean_absolute_error, mean_squared_error
    4. import tensorflow as tf
    5. from tensorflow.python.keras.models import Model
    6. from tensorflow.python.keras.layers import Input, LSTM, Dense, Dropout, Flatten
    7. from tensorflow.python.keras.optimizers import adam_v2
    8.  
    9. # 读取数据
    10. data = pd.read_csv('data.csv')
    11. data['time'] = pd.to_datetime(data['time'], format='%b-%y')
    12.  
    13. n = 6
    14. m = 2
    15.  
    16. # 创建滞后期特征
    17. for i in range(n, 0, -1):
    18.     data[f'lag_{i}'] = data['incidence'].shift(n - i + 1)
    19.  
    20. data = data.dropna().reset_index(drop=True)
    21.  
    22. train_data = data[(data['time'] >= '2004-01-01') & (data['time'] <= '2011-12-31')]
    23. validation_data = data[(data['time'] >= '2012-01-01') & (data['time'] <= '2012-12-31')]
    24.  
    25. # 准备训练数据
    26. X_train = []
    27. y_train = []
    28.  
    29. for i in range(len(train_data) - n - m + 1):
    30.     X_train.append(train_data.iloc[i+n-1][[f'lag_{j}' for j in range(1, n+1)]].values)
    31.     y_train.append(train_data.iloc[i+n:i+n+m]['incidence'].values)
    32.  
    33. X_train = np.array(X_train)
    34. y_train = np.array(y_train)
    35. X_train = X_train.astype(np.float32)
    36. y_train = y_train.astype(np.float32)
    37.  
    38. # 构建LSTM模型
    39. inputs = Input(shape=(n, 1))
    40. x = LSTM(64, return_sequences=True)(inputs)
    41. x = LSTM(32)(x)
    42. x = Dense(50, activation='relu')(x)
    43. x = Dropout(0.1)(x)
    44. outputs = Dense(m)(x)
    45.  
    46. model = Model(inputs=inputs, outputs=outputs)
    47.  
    48. model.compile(optimizer=adam_v2.Adam(learning_rate=0.001), loss='mse')
    49.  
    50. # 训练模型
    51. model.fit(X_train, y_train, epochs=200, batch_size=32, verbose=0)
    52.  
    53. def lstm_rolling_forecast(data, model, n, m):
    54.     y_pred = []
    55.  
    56.     for i in range(len(data) - n):
    57.         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)
    58.         pred = model.predict(input_data)
    59.         y_pred.extend(pred[0])
    60.  
    61.     for i in range(1, m):
    62.         for j in range(len(y_pred) - i):
    63.             y_pred[j+i] = (y_pred[j+i] + y_pred[j]) / 2
    64.  
    65.     return np.array(y_pred)
    66.  
    67. # Predict for train_data and validation_data
    68. y_train_pred_lstm = lstm_rolling_forecast(train_data, model, n, m)[:len(y_train)]
    69. y_validation_pred_lstm = lstm_rolling_forecast(validation_data, model, n, m)[:len(validation_data) - n]
    70.  
    71. # Calculate performance metrics for train_data
    72. mae_train = mean_absolute_error(train_data['incidence'].values[n:len(y_train_pred_lstm)+n], y_train_pred_lstm)
    73. mape_train = np.mean(np.abs((train_data['incidence'].values[n:len(y_train_pred_lstm)+n] - y_train_pred_lstm) / train_data['incidence'].values[n:len(y_train_pred_lstm)+n]))
    74. mse_train = mean_squared_error(train_data['incidence'].values[n:len(y_train_pred_lstm)+n], y_train_pred_lstm)
    75. rmse_train = np.sqrt(mse_train)
    76.  
    77. # Calculate performance metrics for validation_data
    78. mae_validation = mean_absolute_error(validation_data['incidence'].values[n:len(y_validation_pred_lstm)+n], y_validation_pred_lstm)
    79. mape_validation = np.mean(np.abs((validation_data['incidence'].values[n:len(y_validation_pred_lstm)+n] - y_validation_pred_lstm) / validation_data['incidence'].values[n:len(y_validation_pred_lstm)+n]))
    80. mse_validation = mean_squared_error(validation_data['incidence'].values[n:len(y_validation_pred_lstm)+n], y_validation_pred_lstm)
    81. rmse_validation = np.sqrt(mse_validation)
    82.  
    83. print("训练集：", mae_train, mape_train, mse_train, rmse_train)
    84. print("验证集：", mae_validation, mape_validation, mse_validation, rmse_validation)

    结果：

    （4）多步滚动预测-vol. 2

    1. import pandas as pd
    2. import numpy as np
    3. from sklearn.model_selection import train_test_split
    4. from sklearn.metrics import mean_absolute_error, mean_squared_error
    5. from tensorflow.python.keras.models import Sequential, Model
    6. from tensorflow.python.keras.layers import Dense, LSTM, Input
    7. from tensorflow.python.keras.optimizers import adam_v2
    8.  
    9. # Loading and preprocessing the data
    10. data = pd.read_csv('data.csv')
    11. data['time'] = pd.to_datetime(data['time'], format='%b-%y')
    12.  
    13. n = 6
    14. m = 2
    15.  
    16. # 创建滞后期特征
    17. for i in range(n, 0, -1):
    18.     data[f'lag_{i}'] = data['incidence'].shift(n - i + 1)
    19.  
    20. data = data.dropna().reset_index(drop=True)
    21.  
    22. train_data = data[(data['time'] >= '2004-01-01') & (data['time'] <= '2011-12-31')]
    23. validation_data = data[(data['time'] >= '2012-01-01') & (data['time'] <= '2012-12-31')]
    24.  
    25. # 只对X_train、y_train、X_validation取奇数行
    26. X_train = train_data[[f'lag_{i}' for i in range(1, n+1)]].iloc[::2].reset_index(drop=True).values
    27. X_train = X_train.reshape(X_train.shape[0], X_train.shape[1], 1)
    28.  
    29. y_train_list = [train_data['incidence'].shift(-i) for i in range(m)]
    30. y_train = pd.concat(y_train_list, axis=1)
    31. y_train.columns = [f'target_{i+1}' for i in range(m)]
    32. y_train = y_train.iloc[::2].reset_index(drop=True).dropna().values[:, 0]
    33.  
    34. X_validation = validation_data[[f'lag_{i}' for i in range(1, n+1)]].iloc[::2].reset_index(drop=True).values
    35. X_validation = X_validation.reshape(X_validation.shape[0], X_validation.shape[1], 1)
    36.  
    37. y_validation = validation_data['incidence'].values
    38.  
    39. # Building the LSTM model
    40. inputs = Input(shape=(n, 1))
    41. x = LSTM(50, activation='relu')(inputs)
    42. x = Dense(50, activation='relu')(x)
    43. outputs = Dense(1)(x)
    44.  
    45. model = Model(inputs=inputs, outputs=outputs)
    46. optimizer = adam_v2.Adam(learning_rate=0.001)
    47. model.compile(optimizer=optimizer, loss='mse')
    48.  
    49. # Train the model
    50. model.fit(X_train, y_train, epochs=200, batch_size=32, verbose=0)
    51.  
    52. # Predict on validation set
    53. y_validation_pred = model.predict(X_validation).flatten()
    54.  
    55. # Compute metrics for validation set
    56. mae_validation = mean_absolute_error(y_validation[:len(y_validation_pred)], y_validation_pred)
    57. mape_validation = np.mean(np.abs((y_validation[:len(y_validation_pred)] - y_validation_pred) / y_validation[:len(y_validation_pred)]))
    58. mse_validation = mean_squared_error(y_validation[:len(y_validation_pred)], y_validation_pred)
    59. rmse_validation = np.sqrt(mse_validation)
    60.  
    61. # Predict on training set
    62. y_train_pred = model.predict(X_train).flatten()
    63.  
    64. # Compute metrics for training set
    65. mae_train = mean_absolute_error(y_train, y_train_pred)
    66. mape_train = np.mean(np.abs((y_train - y_train_pred) / y_train))
    67. mse_train = mean_squared_error(y_train, y_train_pred)
    68. rmse_train = np.sqrt(mse_train)
    69.  
    70. print("验证集：", mae_validation, mape_validation, mse_validation, rmse_validation)
    71. print("训练集：", mae_train, mape_train, mse_train, rmse_train)

    结果：

    （5）多步滚动预测-vol. 3

    1. import pandas as pd
    2. import numpy as np
    3. from sklearn.metrics import mean_absolute_error, mean_squared_error
    4. from tensorflow.python.keras.models import Sequential, Model
    5. from tensorflow.python.keras.layers import Dense, LSTM, Input
    6. from tensorflow.python.keras.optimizers import adam_v2
    7.  
    8. # 数据读取和预处理
    9. data = pd.read_csv('data.csv')
    10. data_y = pd.read_csv('data.csv')
    11. data['time'] = pd.to_datetime(data['time'], format='%b-%y')
    12. data_y['time'] = pd.to_datetime(data_y['time'], format='%b-%y')
    13.  
    14. n = 6
    15.  
    16. for i in range(n, 0, -1):
    17.     data[f'lag_{i}'] = data['incidence'].shift(n - i + 1)
    18.  
    19. data = data.dropna().reset_index(drop=True)
    20. train_data = data[(data['time'] >= '2004-01-01') & (data['time'] <= '2011-12-31')]
    21. X_train = train_data[[f'lag_{i}' for i in range(1, n+1)]]
    22. m = 3
    23.  
    24. X_train_list = []
    25. y_train_list = []
    26.  
    27. for i in range(m):
    28.     X_temp = X_train
    29.     y_temp = data_y['incidence'].iloc[n + i:len(data_y) - m + 1 + i]
    30.     
    31.     X_train_list.append(X_temp)
    32.     y_train_list.append(y_temp)
    33.  
    34. for i in range(m):
    35.     X_train_list[i] = X_train_list[i].iloc[:-(m-1)].values
    36.     X_train_list[i] = X_train_list[i].reshape(X_train_list[i].shape[0], X_train_list[i].shape[1], 1)
    37.     y_train_list[i] = y_train_list[i].iloc[:len(X_train_list[i])].values
    38.  
    39. # 模型训练
    40. models = []
    41. for i in range(m):
    42.     # Building the LSTM model
    43.     inputs = Input(shape=(n, 1))
    44.     x = LSTM(50, activation='relu')(inputs)
    45.     x = Dense(50, activation='relu')(x)
    46.     outputs = Dense(1)(x)
    47.  
    48.     model = Model(inputs=inputs, outputs=outputs)
    49.     optimizer = adam_v2.Adam(learning_rate=0.001)
    50.     model.compile(optimizer=optimizer, loss='mse')
    51.     model.fit(X_train_list[i], y_train_list[i], epochs=200, batch_size=32, verbose=0)
    52.     models.append(model)
    53.  
    54. validation_start_time = train_data['time'].iloc[-1] + pd.DateOffset(months=1)
    55. validation_data = data[data['time'] >= validation_start_time]
    56. X_validation = validation_data[[f'lag_{i}' for i in range(1, n+1)]].values
    57. X_validation = X_validation.reshape(X_validation.shape[0], X_validation.shape[1], 1)
    58.  
    59. y_validation_pred_list = [model.predict(X_validation) for model in models]
    60. y_train_pred_list = [model.predict(X_train_list[i]) for i, model in enumerate(models)]
    61.  
    62. def concatenate_predictions(pred_list):
    63.     concatenated = []
    64.     for j in range(len(pred_list[0])):
    65.         for i in range(m):
    66.             concatenated.append(pred_list[i][j])
    67.     return concatenated
    68.  
    69. y_validation_pred = np.array(concatenate_predictions(y_validation_pred_list))[:len(validation_data['incidence'])]
    70. y_train_pred = np.array(concatenate_predictions(y_train_pred_list))[:len(train_data['incidence']) - m + 1]
    71. y_validation_pred = y_validation_pred.flatten()
    72. y_train_pred = y_train_pred.flatten()
    73.  
    74. mae_validation = mean_absolute_error(validation_data['incidence'], y_validation_pred)
    75. mape_validation = np.mean(np.abs((validation_data['incidence'] - y_validation_pred) / validation_data['incidence']))
    76. mse_validation = mean_squared_error(validation_data['incidence'], y_validation_pred)
    77. rmse_validation = np.sqrt(mse_validation)
    78.  
    79. mae_train = mean_absolute_error(train_data['incidence'][:-(m-1)], y_train_pred)
    80. mape_train = np.mean(np.abs((train_data['incidence'][:-(m-1)] - y_train_pred) / train_data['incidence'][:-(m-1)]))
    81. mse_train = mean_squared_error(train_data['incidence'][:-(m-1)], y_train_pred)
    82. rmse_train = np.sqrt(mse_train)
    83.  
    84. print("验证集：", mae_validation, mape_validation, mse_validation, rmse_validation)
    85. print("训练集：", mae_train, mape_train, mse_train, rmse_train)

    结果：

    三、数据

    链接：https://pan.baidu.com/s/1EFaWfHoG14h15KCEhn1STg?pwd=q41n

    提取码：q41n

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  • 原文地址：https://blog.csdn.net/qq_30452897/article/details/133971139