Statistical divergences in high-dimensional hypothesis testing and a modern technique for estimating them

TL;DR

This paper introduces a modern approach to high-dimensional hypothesis testing using statistical divergences, leveraging functional optimization techniques to estimate divergences without likelihood functions, demonstrated through a physics-based example.

Contribution

It presents a novel method for estimating statistical divergences in high-dimensional data using functional optimization, enabling hypothesis testing without likelihood functions.

Findings

Effective divergence estimation from samples

Implementation of a two-sample test in practice

Code availability for reproducibility

Abstract

Hypothesis testing in high dimensional data is a notoriously difficult problem without direct access to competing models' likelihood functions. This paper argues that statistical divergences can be used to quantify the difference between the population distributions of observed data and competing models, justifying their use as the basis of a hypothesis test. We go on to point out how modern techniques for functional optimization let us estimate many divergences, without the need for population likelihood functions, using samples from two distributions alone. We use a physics-based example to show how the proposed two-sample test can be implemented in practice, and discuss the necessary steps required to mature the ideas presented into an experimental framework. The code used has been made available for others to use.