Estimating Real Log Canonical Thresholds
This work addresses a bottleneck in Bayesian model selection for statisticians and machine learning practitioners by enabling broader use of sBIC, though it is incremental as it builds on existing methods like WBIC and sBIC.
The paper tackles the problem of estimating real log canonical thresholds, which are needed for the singular Bayesian information criterion (sBIC) to approximate log marginal likelihoods in model selection, by proposing a new estimator based on thermodynamic integration variance. The result shows improved performance in simulation studies and real data applications, making sBIC more widely applicable.
Evaluation of the marginal likelihood plays an important role in model selection problems. The widely applicable Bayesian information criterion (WBIC) and singular Bayesian information criterion (sBIC) give approximations to the log marginal likelihood, which can be applied to both regular and singular models. When the real log canonical thresholds are known, the performance of sBIC is considered to be better than that of WBIC, but only few real log canonical thresholds are known. In this paper, we propose a new estimator of the real log canonical thresholds based on the variance of thermodynamic integration with an inverse temperature. In addition, we propose an application to make sBIC widely applicable. Finally, we investigate the performance of the estimator and model selection by simulation studies and application to real data.