On a fast consistent selection of nested models with possibly unnormalized probability densities

Abstract

Models with unnormalized probability density functions are ubiquitous in statistics, artificial intelligence and many other fields. However, they face significant challenges in model selection if the normalizing constants are intractable. Existing methods to address this issue often incur high computational costs, either due to numerical approximations of normalizing constants or evaluation of bias corrections in information criteria. In this paper, we propose a novel and fast selection criterion, MIC, for nested models of possibly dependent data, allowing direct data sampling from a possibly unnormalized probability density function. With a suitable multiplying factor depending only on the sample size and the model complexity, MIC gives a consistent selection under mild regularity conditions and is computationally efficient. Extensive simulation studies and real-data applications demonstrate the efficacy of MIC in the selection of nested models with unnormalized probability densities.