python 代码实现Uplift model for multiple correlated binary responses WITH LOW-RANK REGULARIZATION logistic regression

Sure, here is an example Python code for Uplift model with low-rank regularization logistic regression for multiple correlated binary responses:

import numpy as np
from sklearn.linear_model import LogisticRegression

# define the Uplift model with low-rank regularization logistic regression
class UpliftLowRankLogisticRegression:
    def __init__(self, rank=5, alpha=1.0):
        self.rank = rank
        self.alpha = alpha
        self.models = []
        self.w = None
        
    def fit(self, X, y, t):
        # calculate the treatment and control groups
        X_treatment = X[t == 1]
        y_treatment = y[t == 1]
        X_control = X[t == 0]
        y_control = y[t == 0]
        
        # fit the logistic regression model for each response
        for i in range(y.shape[1]):
            model = LogisticRegression(penalty='l2', C=self.alpha)
            model.fit(np.hstack((X_treatment, y_treatment[:, i].reshape(-1, 1))),
                      y_treatment[:, i])
            self.models.append(model)
        
        # use SVD to learn the low-rank representation w
        U, S, Vt = np.linalg.svd(y_control - self.predict(X_control))
        self.w = Vt[:self.rank].T
        
    def predict(self, X):
        # calculate the uplift score for each response
        uplift_scores = np.zeros((X.shape[0], len(self.models)))
        for i, model in enumerate(self.models):
            uplift_scores[:, i] = model.predict_proba(X)[:, 1]
        # calculate the predicted response for the control group
        y_control_pred = np.dot(X, self.w)
        # calculate the predicted response for the treatment group
        y_treatment_pred = y_control_pred + uplift_scores
        # return the predicted response matrix
        return np.vstack((y_control_pred, y_treatment_pred))

The `UpliftLowRankLogisticRegression` class takes two hyperparameters: `rank` for the rank of the low-rank representation w and `alpha` for the regularization strength of logistic regression. In the `fit` method, the treatment and control groups are separated, and logistic regression models are fitted for each response using the treatment group. Then, SVD is used to learn the low-rank representation w from the predicted responses of the control group. In the `predict` method, the uplift scores for each response are calculated using the logistic regression models and added to the predicted responses of the control group to obtain the predicted responses of the treatment group. The predicted response matrix is returned by stacking the predicted responses of the control and treatment groups vertically.