Hidden Gibbs random fields model selection using Block Likelihood Information Criterion

TL;DR

This paper introduces the Block Likelihood Information Criterion (BLIC), an approximate model selection method for Gibbs random fields that addresses the intractability of likelihood evaluation by partitioning the lattice into blocks.

Contribution

The paper proposes a novel approximate BIC based on block partitioning to enable efficient model selection in Gibbs random fields with intractable likelihoods.

Findings

BLIC outperforms ABC algorithms in efficiency and reliability

The method effectively selects dependency structures and latent states

Partitioning improves approximation accuracy for model selection

Abstract

Performing model selection between Gibbs random fields is a very challenging task. Indeed, due to the Markovian dependence structure, the normalizing constant of the fields cannot be computed using standard analytical or numerical methods. Furthermore, such unobserved fields cannot be integrated out and the likelihood evaluztion is a doubly intractable problem. This forms a central issue to pick the model that best fits an observed data. We introduce a new approximate version of the Bayesian Information Criterion. We partition the lattice into continuous rectangular blocks and we approximate the probability measure of the hidden Gibbs field by the product of some Gibbs distributions over the blocks. On that basis, we estimate the likelihood and derive the Block Likelihood Information Criterion (BLIC) that answers model choice questions such as the selection of the dependency structure or the number of latent states. We study the performances of BLIC for those questions. In addition, we present a comparison with ABC algorithms to point out that the novel criterion offers a better trade-off between time efficiency and reliable results.