Discrete Graphical Models — An Optimization Perspective

Learning discrete decomposable graphical models via constraint optimization

Statistical model learning problems are traditionally solved using either heuristic greedy optimization or stochastic simulation, such as Markov chain Monte Carlo or simulated annealing. Recently, there has been an increasing interest in the use of combinatorial search methods, including those based on computational logic. Some of these methods are particularly attractive since they can also be...

State estimation in discrete graphical models

p(X1:D|G, θ) (1) whereG is the graph structure (either directed or undirected or both), and θ are the parameters. In Bayesian modeling, we treat the parameters as random variables as well, but they are in turn conditioned on fixed hyper parameters α: p(X1:D, θ|G,α) (2) Clearly this can be represented as in Equation 1 by appropriately redefining X and θ. It will also be notationally helpful to d...

Efficient Model Determination for Discrete Graphical Models

MCMC model determination for discrete graphical models

In this paper we compare two alternative MCMC samplers for the Bayesian analysis of discrete graphical models; we present both a hierarchical and a nonhierarchical version of them. We Žrst consider the MC3 algorithm by Madigan and York (1995) for which we propose an extension that allows for a hierarchical prior on the cell counts. We then describe a novel methodology based on a reversible jump...

Graphical models for discrete hidden Markov models in speech recognition

Emission probability distributions in speech recognition have been traditionally associated to continuous random variables. The most successful models have been the mixtures of Gaussians in the states of the hidden Markov models to generate/capture observations. In this work we show how graphical models can be used to extract the joint information of more than two features. This is possible if ...