Large Deviation Analysis of Score-Based Hypothesis Testing

Abstract

Score-based statistical models play an important role in modern machine learning, statistics, and signal processing. For hypothesis testing, a score-based hypothesis test is proposed in Wu et al., (2022). We analyze the performance of this score-based hypothesis testing procedure and derive upper bounds on the probabilities of its Type I and II errors. We prove that the exponents of our error bounds are asymptotically (in the number of samples) tight for the case of simple null and alternative hypotheses. We also calculate these error exponents explicitly in specific cases. We then provide numerical studies for various scenarios of interest and show that the analytical estimates of the error probabilities provide a good approximation to the true error probabilities estimated via simulations.

Keywords

• Hypothesis testing
• score matching
• unnormalized statistical models
• error exponents