Distributed parameter estimation of discrete hierarchical models via marginal likelihoods

Abstract

We consider discrete graphical models Markov with respect to a graph $G$ and propose two distributed marginal methods to estimate the maximum likelihood estimate of the canonical parameter of the model. Both methods are based on a relaxation of the marginal likelihood obtained by considering the density of the variables represented by a vertex $v$ of $G$ and a neighborhood. The two methods differ by the size of the neighborhood of $v$. We show that the estimates are consistent and that those obtained with the larger neighborhood have smaller asymptotic variance than the ones obtained through the smaller neighborhood.

21 pages, 7 figures

References in corpus (2)

• Maximum likelihood estimation in log-linear models
• Distributed Parameter Estimation via Pseudo-likelihood

Cited by in corpus (1)

• Marginal Likelihoods for Distributed Parameter Estimation of Gaussian Graphical Models