Decomposed Normalized Maximum Likelihood Codelength Criterion for Selecting Hierarchical Latent Variable Models

We propose a new model selection criterion based on the minimum description length principle in a name of the decomposed normalized maximum likelihood criterion. Our criterion can be applied to a large class of hierarchical latent variable models, such as the Naive Bayes models, stochastic block models and latent Dirichlet allocations, for which many conventional information criteria cannot be straightforwardly applied due to irregularity of latent variable models. Our method also has an advantage that it can be exactly evaluated without asymptotic approximation with small time complexity. Our experiments using synthetic and real data demonstrated validity of our method in terms of computational efficiency and model selection accuracy, while our criterion especially dominated the other criteria when sample size is small and when data are noisy.