Model selection for discrete Markov random fields on graphs

• Ano de defesa: 2016
• Autor(a) principal: Frondana, Iara Moreira
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Campos aleatórios Markovianos discretos; Critério de Informação Bayesiano; Discrete Markov random fields; Grafos simples não-dirigidos; Model selection Bayesian information criterion; Seleção de modelos; Simlple undirected graphs
• Link de acesso: http://www.teses.usp.br/teses/disponiveis/45/45133/tde-02022018-151123/

In this thesis we propose to use a penalized maximum conditional likelihood criterion to estimate the graph of a general discrete Markov random field. We prove the almost sure convergence of the estimator of the graph in the case of a finite or countable infinite set of variables. Our method requires minimal assumptions on the probability distribution and contrary to other approaches in the literature, the usual positivity condition is not needed. We present several examples with a finite set of vertices and study the performance of the estimator on simulated data from theses examples. We also introduce an empirical procedure based on k-fold cross validation to select the best value of the constant in the estimators definition and show the application of this method in two real datasets.