A Nonparametric Approach to High-dimensional k-sample Comparison Problems

TL;DR

This paper introduces a new nonparametric method for high-dimensional k-sample comparison, leveraging spectral graph theory to create practical, distribution-free tests with strong performance in diverse real-world scenarios.

Contribution

The paper presents a novel nonparametric testing framework for high-dimensional k-sample problems, connecting spectral graph theory with statistical testing.

Findings

Method performs well across various realistic datasets

Tests are easy to implement and distribution-free

Possesses desirable statistical properties

Abstract

High-dimensional k-sample comparison is a common applied problem. We construct a class of easy-to-implement nonparametric distribution-free tests based on new tools and unexplored connections with spectral graph theory. The test is shown to possess various desirable properties along with a characteristic exploratory flavor that has practical consequences. The numerical examples show that our method works surprisingly well under a broad range of realistic situations.