Global and Local Two-Sample Tests via Regression

TL;DR

This paper introduces a regression-based framework for two-sample testing that can identify both global and local differences between complex multivariate distributions, improving interpretability and practical applicability.

Contribution

It presents a novel regression approach enabling local two-sample tests, extending beyond traditional global tests to reveal detailed distributional differences.

Findings

The method effectively detects local differences in simulated data.

It performs competitively with existing tests in various scenarios.

Applied to astronomy data, it uncovers meaningful local distributional variations.

Abstract

Two-sample testing is a fundamental problem in statistics. Despite its long history, there has been renewed interest in this problem with the advent of high-dimensional and complex data. Specifically, in the machine learning literature, there have been recent methodological developments such as classification accuracy tests. The goal of this work is to present a regression approach to comparing multivariate distributions of complex data. Depending on the chosen regression model, our framework can efficiently handle different types of variables and various structures in the data, with competitive power under many practical scenarios. Whereas previous work has been largely limited to global tests which conceal much of the local information, our approach naturally leads to a local two-sample testing framework in which we identify local differences between multivariate distributions with statistical confidence. We demonstrate the efficacy of our approach both theoretically and empirically, under some well-known parametric and nonparametric regression methods. Our proposed methods are applied to simulated data as well as a challenging astronomy data set to assess their practical usefulness.