[4G4-OS-26a] OS-26

2:30 PM - 2:45 PM JST(5:30 AM - 5:45 AM UTC)

[4G4-OS-26a-04] A New Relationship Between WAIC and WBIC and its Application to Bayesian Inference

〇Naoki Hayashi Hayashi¹, Takuro Kutsuna¹, Sawa Takamuku² (1. Toyota Central R&D Labs., Inc., 2. AISIN CORPORATION)

Keywords:

singular learning theory,Bayesian inference,information criterion,model selection,real log canonical threshold

For the realization of a human-centered future society, AI systems must be evaluated not only by predictive accuracy but also by how plausible their generalization performance can be assessed and communicated. Thus, it is important to establish a rigorous theoretical foundation. Many statistical models used in machine learning are singular, meaning that conventional information criteria based on regular asymptotic theory are not appropriate. For such models, WAIC and WBIC have been established as alternatives; however, they rely on posterior distributions defined at different inverse temperatures, which usually requires separate sampling procedures. This study derives an asymptotic connection between WAIC and WBIC within singular learning theory. Based on this relationship, WAIC can be approximated using the posterior distribution employed for WBIC, without additional sampling. The result provides insight into the asymptotic structure of these criteria and suggests a potential way to reduce computational cost in Bayesian model selection for singular models.