Approximate Bayes model selection procedures for Gibbs-Markov random fields

Seymour, Lynné; Ji, Chuanshu

doi:10.1016/0378-3758(95)00071-2

Cited by 11 publications

(2 citation statements)

References 25 publications

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“…The difficulty in the context of hidden Markov random fields lies in that the maximized log-likelihood part in BIC involves Markov distributions whose exact computation requires an exponential amount of time. As regards observed Markov random fields selection, Ji and Seymour [9] propose a consistent procedure based on penalized Besag pseudolikelihood [10], [11] study a Markov Chain Monte Carlo (MCMC) approximation of BIC. When the fields are hidden, little has been done to address the selection problem.…”

Section: Introductionmentioning

confidence: 99%

Hidden markov random field model selection criteria based on mean field-like approximations

Forbes

Peyrard

2003

IEEE Trans. Pattern Anal. Machine Intell.

107

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Hidden Markov random fields appear naturally in problems such as image segmentation, where an unknown class assignment has to be estimated from the observations at each pixel. Choosing the probabilistic model that best accounts for the observations 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 Schwarz (1978), 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, also called partition functions, instead of Markov distributions. It enables us to use finer mean field approximations and to 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.

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Section: Introductionmentioning

confidence: 99%

Hidden markov random field model selection criteria based on mean field-like approximations

Forbes

Peyrard

2003

IEEE Trans. Pattern Anal. Machine Intell.

107

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show abstract

“…The criterion is a simple penalized function of the maximized log‐likelihood, which, in the context of hidden Gibbs random fields, cannot be computed because it requires integrating the intractable Gibbs distribution over the latent space configurations. As regards the simpler case of observed Markov random field, solutions have been brought by penalized pseudolikelihood (Ji and Seymour, ) or Markov chain Monte Carlo (MCMC) approximation of BIC (Seymour and Ji, ). To circumvent the computational difficulties in the hidden case, little has been done before the work of Stanford and Raftery () and Forbes and Peyrard ().…”

Section: Introductionmentioning

confidence: 99%

Hidden Gibbs random fields model selection using Block Likelihood Information Criterion

Stoehr

Marin

Pudlo

2016

Stat

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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.

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2010

Spatial Statistics and Spatio‐Temporal Data

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Approximate Bayes model selection procedures for Gibbs-Markov random fields

Cited by 11 publications

References 25 publications

Hidden markov random field model selection criteria based on mean field-like approximations

Hidden markov random field model selection criteria based on mean field-like approximations

Hidden Gibbs random fields model selection using Block Likelihood Information Criterion

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