Skip to Main content Skip to Navigation
Reports

Hidden Markov Models Selection Criteria based on Mean Field-like approximations

Florence Forbes 1 Nathalie Peyrard 2
1 IS2 - Statistical Inference for Industry and Health
Inria Grenoble - Rhône-Alpes, LBBE - Laboratoire de Biométrie et Biologie Evolutive - UMR 5558
2 VISTA - Vision spatio-temporelle et active
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
Abstract : Hidden Markov random fields appear naturally in problems such as image segmentation where an unknown class assignment has to be estimated from the observations for each pixel. Choosing the probabilistic model that best accounts for the observed data is an important first step for the quality of the subsequent estimation and analysis. A commonly used selection criterion is the Bayesian Information Criterion (BIC) of \citeN{schwarz} but for hidden Markov random fields, its exact computation is not tractable due to the dependence structure induced by the Markov model. We propose approximations of BIC based on the mean field principle of statistical physics. The mean field theory provides approximations of Markov random fields by systems of independent variables leading to tractable computations. Using this principle, we first derive a class of criteria by approximating the Markov distribution in the usual BIC expression as a penalized likelihood. We then rewrite BIC in terms of normalizing constants (partition functions) instead of Markov distributions, which enables us to use finer mean field approximations and derive other criteria using optimal lower bounds for the normalizing constants. To illustrate the performance of our partition function-based approximation of BIC as a model selection criterion, we focus on the preliminary issue of choosing the number of classes before the segmentation task. Experiments on simulated and real data point out our criterion as promising: it takes spatial information into account through the Markov model and improves the results obtained with BIC for independent mixture models.
Document type :
Reports
Complete list of metadata

https://hal.inria.fr/inria-00072217
Contributor : Rapport de Recherche Inria <>
Submitted on : Tuesday, May 23, 2006 - 8:07:51 PM
Last modification on : Thursday, January 7, 2021 - 4:39:05 PM
Long-term archiving on: : Sunday, April 4, 2010 - 10:58:50 PM

Identifiers

  • HAL Id : inria-00072217, version 1

Citation

Florence Forbes, Nathalie Peyrard. Hidden Markov Models Selection Criteria based on Mean Field-like approximations. [Research Report] RR-4371, INRIA. 2002. ⟨inria-00072217⟩

Share

Metrics

Record views

328

Files downloads

605