Diffusion-Based Hypothesis Testing and Change-Point Detection

TL;DR

This paper extends score-based hypothesis testing and change-point detection methods into diffusion-based analogs, providing theoretical performance analysis and numerical optimization to improve their effectiveness.

Contribution

It introduces diffusion-based versions of hypothesis testing and change-point detection, with theoretical performance quantification and a numerical optimization approach for the weight matrix.

Findings

Diffusion-based algorithms outperform score-based methods in certain scenarios.

Theoretical analysis quantifies the performance bounds of the proposed methods.

Numerical simulations demonstrate the advantages of diffusion-based approaches.

Abstract

Score-based methods have recently seen increasing popularity in modeling and generation. Methods have been constructed to perform hypothesis testing and change-point detection with score functions, but these methods are in general not as powerful as their likelihood-based peers. Recent works consider generalizing the score-based Fisher divergence into a diffusion-divergence by transforming score functions via multiplication with a matrix-valued function or a weight matrix. In this paper, we extend the score-based hypothesis test and change-point detection stopping rule into their diffusion-based analogs. Additionally, we theoretically quantify the performance of these diffusion-based algorithms and study scenarios where optimal performance is achievable. We propose a method of numerically optimizing the weight matrix and present numerical simulations to illustrate the advantages of diffusion-based algorithms.