Information criteria for non-normalized models
This work addresses a gap in model selection for non-normalized models, which is important for statisticians and machine learning practitioners dealing with complex data, though it is incremental as it builds on existing estimation methods.
The authors tackled the problem of model selection for non-normalized statistical models, which lack tractable normalization constants, by developing information criteria for models estimated via noise contrastive estimation or score matching, and demonstrated through simulations and real data that these criteria enable data-driven selection of appropriate models.
Many statistical models are given in the form of non-normalized densities with an intractable normalization constant. Since maximum likelihood estimation is computationally intensive for these models, several estimation methods have been developed which do not require explicit computation of the normalization constant, such as noise contrastive estimation (NCE) and score matching. However, model selection methods for general non-normalized models have not been proposed so far. In this study, we develop information criteria for non-normalized models estimated by NCE or score matching. They are approximately unbiased estimators of discrepancy measures for non-normalized models. Simulation results and applications to real data demonstrate that the proposed criteria enable selection of the appropriate non-normalized model in a data-driven manner.