Gaussian Markov Random Fields for Discrete Optimization via Simulation: Framework and Algorithms

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...

Subset Selection for Gaussian Markov Random Fields

Given a Gaussian Markov random field, we consider the problem of selecting a subset of variables to observe which minimizes the total expected squared prediction error of the unobserved variables. We first show that finding an exact solution is NP-hard even for a restricted class of Gaussian Markov random fields, called Gaussian free fields, which arise in semi-supervised learning and computer ...

Gaussian Markov Random Fields: Theory and Applications

Approximating Hidden Gaussian Markov Random Fields

This paper discusses how to construct approximations to a unimodal hidden Gaussian Markov random field on a graph of dimensionnwhen the likelihood consists of mutually independent data. We demonstrate that a class of non-Gaussian approximations can be constructed for a wide range of likelihood models. They have the appealing properties that exact samples can be drawn from them, the normalisatio...

A Fast and Exact Simulation Algorithm for General Gaussian Markov Random Fields

This paper presents a fast and exact simulation algorithm for a general Gaussian Markov Random Field (GMRF) defined on a lattice, . For a neighborhood, the algorithm has initializationcost of flops and exact samples are then available using flops. Conditioned samples on general constraints costs only extra flops. The algorithm is easy to generalize to non-rectangular lattices, compute the log-l...