A Decomposition Theorem for Binary Markov Random Fields

Strong Spatial Mixing for Binary Markov Random Fields

The remarkable contribution by Weitz gives a general framework to establish the strong spatial mixing property of Gibbs measures. In light of Weitz’s work, we prove the strong spatial mixing for binary Markov random fields under the condition that the ‘external field’ is uniformly large or small by turning them into a corresponding Ising model. Our proof is done through a ‘path’ characterizatio...

High-Dimensional Structured Feature Screening Using Binary Markov Random Fields

Feature screening is a useful feature selection approach for high-dimensional data when the goal is to identify all the features relevant to the response variable. However, common feature screening methods do not take into account the correlation structure of the covariate space. We propose the concept of a feature relevance network, a binary Markov random field to represent the relevance of ea...

Binary pattern recognition using Markov random fields and HMMs

In this paper we present a stochastic framework for the recognition of binary random patterns which advantageously combine hmms and Markov random elds (mrfs). The hmm component of the model analyzes the image along one direction, in a speci c state observation probability given by the product of causal mrf-like pixel conditional probabilities. Aspects concerning de nition, training and recognit...

Optimization of Discrete Markov Random Fields via Dual Decomposition

A new message-passing scheme for MRF optimization is proposed in this paper. This scheme inherits better theoretical properties than all other state-of-the-art message passing methods and in practice performs equally well/outperforms them. It is based on the very powerful technique of Dual Decomposition [1] and leads to an elegant and general framework for understanding/designing message-passin...

Image Segmentation Using Binary Tree Structured Markov Random Fields