Open Access
February, 1993 A Variational Method for Estimating the Parameters of MRF from Complete or Incomplete Data
Murilo P. Almeida, Basilis Gidas
Ann. Appl. Probab. 3(1): 103-136 (February, 1993). DOI: 10.1214/aoap/1177005510


We introduce a new method (to be referred to as the variational method, VM) for estimating the parameters of Gibbs distributions with random variables ("spins") taking values in a Euclidean space $\mathbb{R}^n, n \geq 1$, from complete or degraded data. The method applies also to the case of iid random variables governed by exponential families, and appears to be new even in this case. For complete data, the VM is computationally more efficient than, and as reliable as, the maximum pseudo-likelihood method. For incomplete data, the VM leads to an estimation procedure reminiscent of, but simpler than, the EM algorithm. In the former case, we show that under natural assumptions a certain form of the variational estimators is strongly consistent and asymptotically normal. We also present numerical experiments that demonstrate the computational efficiency and accuracy of the variational estimators.


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Murilo P. Almeida. Basilis Gidas. "A Variational Method for Estimating the Parameters of MRF from Complete or Incomplete Data." Ann. Appl. Probab. 3 (1) 103 - 136, February, 1993.


Published: February, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0771.60091
MathSciNet: MR1202518
Digital Object Identifier: 10.1214/aoap/1177005510

Primary: 60K35
Secondary: 60J99 , 62H12 , 62M40

Keywords: asymptotic normality , consistency , Super-stable Gibbs distributions , variational estimators

Rights: Copyright © 1993 Institute of Mathematical Statistics

Vol.3 • No. 1 • February, 1993
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