Distributed parameter estimation of discrete hierarchical models via marginal likelihoods
This work addresses parameter estimation in graphical models for statistical inference, but it appears incremental as it builds on existing marginal likelihood approaches with neighborhood variations.
The authors tackled the problem of estimating parameters in discrete graphical models by proposing two distributed marginal likelihood methods, showing that both yield consistent estimates and the method with a larger neighborhood achieves smaller asymptotic variance.
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.