Model selection for Markov random fields on graphs under a mixing condition

2023/11/03 by Florencia Leonardi, Leonardi, Florencia, Magno T. F. Severino +1
Computer Science · Mathematics · #Bayesian Modeling and Causal Inference #Markov Chains and Monte Carlo Methods #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2311.01999

Abstract

In this work, we propose a global model selection criterion to estimate the graph of conditional dependencies of a random vector based on a finite sample. By global criterion, we mean optimizing a function over the entire set of possible graphs, eliminating the need to estimate the individual neighborhoods and subsequently combine them to estimate the graph. We prove the almost sure convergence of the graph estimator. This convergence holds provided the data is a realization of a multivariate stochastic process that satisfies a mixing condition. To the best of our knowledge, these are the first results to show the consistency of a model selection criterion for Markov random fields on graphs under non-independent data.

Related

• Structure recovery for partially observed discrete Markov random fields on graphs under not necessarily positive distributions
• Reconstruction of Markov Random Fields from Samples: Some Easy Observations and Algorithms
• Graphical Markov models for infinitely many variables
• Latent variable model selection for Gaussian conditional random fields
• Stationary Geometric Graphical Model Selection