MATES: Multi-view Aggregated Two-Sample Test

TL;DR

MATES is a new multi-view approach for two-sample testing that aggregates information from multiple moments and uses graph-based methods to detect complex distributional differences in high-dimensional data.

Contribution

It introduces a novel framework combining multiple moments and graph-based techniques for more powerful two-sample testing in high-dimensional settings.

Findings

Effectively detects subtle distribution differences.

Provides a distribution-free null distribution for error control.

Demonstrates superior performance on real-world data.

Abstract

The two-sample test is a fundamental problem in statistics with a wide range of applications. In the realm of high-dimensional data, nonparametric methods have gained prominence due to their flexibility and minimal distributional assumptions. However, many existing methods tend to be more effective when the two distributions differ primarily in their first and/or second moments. In many real-world scenarios, distributional differences may arise in higher-order moments, rendering traditional methods less powerful. To address this limitation, we propose a novel framework to aggregate information from multiple moments to build a test statistic. Each moment is regarded as one view of the data and contributes to the detection of some specific type of discrepancy, thus allowing the test statistic to capture more complex distributional differences. The novel multi-view aggregated two-sample test (MATES) leverages a graph-based approach, where the test statistic is constructed from the weighted similarity graphs of the pooled sample. Under mild conditions on the multi-view weighted similarity graphs, we establish theoretical properties of MATES, including a distribution-free limiting distribution under the null hypothesis, which enables straightforward type-I error control. Extensive simulation studies demonstrate that MATES effectively distinguishes subtle differences between distributions. We further validate the method on the S&P100 data, showcasing its power in detecting complex distributional variations.