Diffusion-Based Hypothesis Testing and Change-Point Detection
This work addresses the need for more powerful statistical methods in hypothesis testing and change-point detection, though it appears incremental as it builds on existing score-based approaches.
The authors tackled the problem of improving the power of score-based methods for hypothesis testing and change-point detection by extending them into diffusion-based analogs, resulting in algorithms that show advantages in numerical simulations.
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.