Learning Sparse Graph with Minimax Concave Penalty under Gaussian Markov Random Fields

Fast Sparse Gaussian Markov Random Fields Learning Based on Cholesky Factorization

Learning the sparse Gaussian Markov Random Field, or conversely, estimating the sparse inverse covariance matrix is an approach to uncover the underlying dependency structure in data. Most of the current methods solve the problem by optimizing the maximum likelihood objective with a Laplace prior L1 on entries of a precision matrix. We propose a novel objective with a regularization term which ...

Relational Graph Labelling Using Learning Techniques and Markov Random Fields

This paper introduces an approach for handling complex labelling problems driven by local constraints. The purpose is illustrated by two applications: detection of the road network on radar satellite images, and recognition of the cortical sulci on MRI images. Features must be initially extracted from the data to build a “feature graph” with structural relations. The goal is to endow each featu...

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