偏最小二乘法多元线性回归代码

以下是使用偏最小二乘法进行多元线性回归的Python代码示例：

import numpy as np

class PLSRegression():
    def __init__(self, n_components=None):
        self.n_components = n_components

    def fit(self, X, Y):
        n_features = X.shape[1]
        n_outputs = Y.shape[1]
        if not self.n_components:
            self.n_components = min(n_features, n_outputs)

        T = np.zeros((X.shape[0], self.n_components))
        P = np.zeros((n_features, self.n_components))
        Q = np.zeros((n_outputs, self.n_components))
        W = np.zeros((n_features, self.n_components))
        B = np.zeros((n_outputs, self.n_components))

        for i in range(self.n_components):
            t = np.dot(X, Y)[:, 0]
            for j in range(i):
                t -= np.dot(T[:, j], np.dot(P[:, j], np.dot(Q[:, j].T, Y))) / np.dot(T[:, j], T[:, j])
            T[:, i] = t

            p = np.dot(X.T, T[:, i])
            p /= np.dot(p, p)
            P[:, i] = p

            q = np.dot(Y.T, T[:, i])
            q /= np.dot(q, q)
            Q[:, i] = q

        for i in range(self.n_components):
            w = np.dot(X.T, T[:, i])
            w /= np.dot(w, w)
            W[:, i] = w

            b = np.dot(Y.T, T[:, i]) / np.dot(T[:, i], T[:, i])
            B[:, i] = b

            X = X - np.dot(T[:, i].reshape(-1, 1), w.reshape(1, -1))
            Y = Y - np.dot(T[:, i].reshape(-1, 1), b.reshape(1, -1))

        self.P_ = P
        self.Q_ = Q
        self.W_ = W
        self.B_ = B

    def predict(self, X):
        Y_pred = np.dot(X, self.P_)
        Y_pred = np.dot(Y_pred, self.Q_.T)
        Y_pred += self.B_.T
        return Y_pred

其中，fit方法用于拟合模型，predict方法用于预测。输入的X和Y分别为训练数据的特征和标签，输出为预测结果。