应用BRITS算法填补连续缺失值的Python程序

好的，下面是一个应用 BRITS 算法填补连续缺失值的 Python 程序示例：

import numpy as np
from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA
from sklearn.linear_model import LinearRegression
from scipy import stats

def BRITS(data, window=10, num_pc=5):
    """
    使用 BRITS 算法填补连续缺失值
    :param data: 时间序列数据，类型为 numpy 数组
    :param window: 滑动窗口大小，默认为 10
    :param num_pc: 保留主成分的个数，默认为 5
    :return: 填补后的时间序列数据
    """
    # 标准化数据
    scaler = StandardScaler()
    data = scaler.fit_transform(data)

    # 使用 PCA 进行降维
    pca = PCA(n_components=num_pc)
    data_pca = pca.fit_transform(data)

    # 使用滑动窗口分割数据
    num_samples = len(data_pca)
    num_windows = num_samples - window + 1
    windows = np.zeros((num_windows, window, num_pc))
    for i in range(num_windows):
        windows[i] = data_pca[i:i+window]

    # 训练模型并填充缺失值
    filled_data = np.copy(data)
    for i in range(num_windows):
        window_data = windows[i]
        window_data_masked = np.ma.masked_invalid(window_data)
        num_missing = np.sum(window_data_masked.mask)
        if num_missing > 0:
            # 根据前后窗口的数据预测缺失的数据
            prev_window = windows[max(i-1, 0)]
            next_window = windows[min(i+1, num_windows-1)]
            prev_data = prev_window[-1]
            next_data = next_window[0]
            prev_data_masked = np.ma.masked_invalid(prev_data)
            next_data_masked = np.ma.masked_invalid(next_data)
            prev_data_masked = prev_data_masked[~prev_data_masked.mask]
            next_data_masked = next_data_masked[~next_data_masked.mask]
            if prev_data_masked.size > 0 and next_data_masked.size > 0:
                prev_mean = np.mean(prev_data_masked)
                next_mean = np.mean(next_data_masked)
                if np.isnan(prev_mean):
                    prev_mean = next_mean
                elif np.isnan(next_mean):
                    next_mean = prev_mean
                diff = next_mean - prev_mean
                if np.abs(diff) > 1e-6:
                    slope = (next_data - prev_data) / diff
                    intercept = next_data - slope * next_mean
                    missing_idx = np.where(window_data_masked.mask)[0]
                    for j in missing_idx:
                        x = j / (window-1)
                        filled_data[i+j] = scaler.inverse_transform(pca.inverse_transform(slope*x+intercept))
                else:
                    filled_data[i:i+window] = scaler.inverse_transform(pca.inverse_transform(np.mean([prev_data, next_data], axis=0)))

    # 去除因标准化而引入的误差
    filled_data = scaler.inverse_transform(filled_data)

    # 检查是否有超出原始值范围的值
    for i in range(len(filled_data)):
        if np.isnan(filled_data[i]):
            filled_data[i] = data[i]
        elif filled_data[i] < np.min(data):
            filled_data[i] = np.min(data)
        elif filled_data[i] > np.max(data):
            filled_data[i] = np.max(data)

    return filled_data

这个程序使用了一些机器学习工具，比如标准化、PCA 和线性回归等。它的基本思路是将时间序列数据进行降维处理，然后使用滑动窗口的方式对数据进行分割，再使用前后窗口的数据来预测缺失的数据，并填充缺失值。最后，程序还进行了一些额外的处理，比如去除因标准化而引入的误差、检查是否有超出原始值范围的值等。