Two-sample test based on Self-Organizing Maps

TL;DR

This paper proposes using Self-Organizing Maps as a two-sample test that not only detects differences between samples but also provides insights into how they differ, combining classification with interpretability.

Contribution

It introduces a novel approach leveraging Self-Organizing Maps for two-sample testing that offers both discrimination and interpretability.

Findings

SOM-based test can distinguish different populations effectively.

Provides insights into sample differences through visualization.

Combines classification accuracy with interpretability.

Abstract

Machine-learning classifiers can be leveraged as a two-sample statistical test. Suppose each sample is assigned a different label and that a classifier can obtain a better-than-chance result discriminating them. In this case, we can infer that both samples originate from different populations. However, many types of models, such as neural networks, behave as a black-box for the user: they can reject that both samples originate from the same population, but they do not offer insight into how both samples differ. Self-Organizing Maps are a dimensionality reduction initially devised as a data visualization tool that displays emergent properties, being also useful for classification tasks. Since they can be used as classifiers, they can be used also as a two-sample statistical test. But since their original purpose is visualization, they can also offer insights.