Deterministic Gaussian Markov fields

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...

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

Markov Loops, Determinants and Gaussian Fields

The purpose of this note is to explore some simple relations between loop measures, determinants, and Gaussian Markov fields. These relations are related to Dynkin’s isomorphism (cf[1], [8], [5]) . Their potential interest could be suggested by noting that loop measures were defined in [3] for planar Brownian motion and are related to SLE processes (see also [11]). It is also the case for the f...

Modelling Gaussian Fields and Geostatistical Data Using Gaussian Markov Random Fields