Fast high-dimensional mean testing via logistic regression

2026-08-20

AI Summary

本文提出一种基于逻辑回归的高效方法，用于检测高维数据中两个或多个群体均值是否相等，通过Lasso筛选变量并在降维后进行推断。

Abstract

We propose computationally efficient tests for equality of mean vectors of two or more high-dimensional populations. Central to our approach is an equivalence between equality of means and a zero population logistic regression parameter. We establish this equivalence for independently distributed observations without imposing common distributional assumptions across populations. Our procedure uses logistic Lasso to screen informative variables and an unpenalized logistic refit for inference in the reduced dimension, yielding asymptotically correct size and consistency. For a specified two-sample Gaussian submodel and sparse discriminative class, the test also attains the minimax separation rate. The framework extends to multiple populations through multi-class logistic regression. Simulations demonstrate accurate size control, strong power, and favorable computational scaling compared with existing tests under unbalanced designs and variance heterogeneity. Applications to gene-expression data with more than twenty-two thousand variables illustrate the practical scalability of the proposed procedures.

Problem

• high-dimensional
• mean testing
• logistic regression
• equality of means

Innovation

• logistic regression
• high-dimensional mean testing
• Lasso
• minimax separation rate
• multi-class logistic regression