Sampling Strategies for Fast Updating of Gaussian Markov Random Fields

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 ...

Parallelizable Sampling of Markov Random Fields

Markov Random Fields (MRFs) are an important class of probabilistic models which are used for density estimation, classification, denoising, and for constructing Deep Belief Networks. Every application of an MRF requires addressing its inference problem, which can be done using deterministic inference methods or using stochastic Markov Chain Monte Carlo methods. In this paper we introduce a new...

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...

Gaussian Markov Random Fields: Theory and Applications

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...