Distributed parameter estimation of discrete hierarchical models via marginal likelihoods

TL;DR

This paper introduces two distributed methods for estimating parameters in discrete graphical models, leveraging marginal likelihoods over neighborhoods, with larger neighborhoods yielding more precise estimates.

Contribution

The paper proposes novel distributed marginal likelihood methods for parameter estimation in discrete graphical models, demonstrating consistency and improved variance with larger neighborhoods.

Findings

Estimates are consistent across methods.

Larger neighborhoods lead to smaller asymptotic variance.

Methods are applicable to Markov discrete graphical models.

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.