Python code for Uplift model with low-rank regularization logistic regression for multiple correlated binary responses. and calculate Individual Treatment Effect (ITE)

Here is an example Python code for Uplift model with low-rank regularization logistic regression for multiple correlated binary responses and calculating Individual Treatment Effect (ITE).

import numpy as np
from sklearn.linear_model import LogisticRegression
from scipy.optimize import minimize

def fit_low_rank_regression(X, Y, Z, r=10, alpha=0.01):
    n, p = X.shape
    q = Y.shape[1]
    U, s, Vt = np.linalg.svd(Z)
    U = U[:, :r]
    Vt = Vt[:r, :]
    S_inv = np.diag(1/s[:r])
    X_tilde = U.T @ X @ Vt.T
    Y_tilde = U.T @ Y
    model = LogisticRegression(penalty='none', solver='lbfgs')
    beta = np.zeros((p, q))
    for j in range(q):
        beta[:, j] = model.fit(X_tilde, Y_tilde[:, j]).coef_
    beta = Vt.T @ beta @ S_inv
    return beta

def estimate_ite(X, Y, Z, delta):
    p = X.shape[1]
    beta = fit_low_rank_regression(X, Y, Z)
    eta = X @ beta
    Y_pred = np.exp(eta)/(1+np.exp(eta))
    ite = np.zeros(p)
    for i in range(p):
        Y_treat = Y_pred.copy()
        Y_treat[:, i] = np.exp(eta[:, i] + delta)/(1+np.exp(eta[:, i] + delta))
        ite[i] = np.mean(Y_treat - Y_pred)
    return ite

Input:

- `X`: the matrix of features (n x p)
- `Y`: the matrix of binary responses (n x q)
- `Z`: the matrix of treatment indicators (n x r)
- `delta`: the treatment effect for each feature (p x 1)

Output:

- `ite`: the Individual Treatment Effect for each feature (p x 1)

Example usage:

# generate synthetic data
n = 1000
p = 5
q = 3
r = 2
X = np.random.normal(size=(n, p))
Z = np.random.binomial(n=1, p=0.5, size=(n, r))
beta_true = np.random.normal(size=(p, q))
Y_true = (X @ beta_true) * Z + np.random.normal(size=(n, q))
delta_true = np.random.normal(size=(p, 1))

# estimate ITE
ite = estimate_ite(X, Y_true, Z, delta_true)
print(ite)