Some links between conditional and coregionalized multivariate Gaussian Markov random fields

Markov Random Fields and Conditional Random Fields

Markov chains provided us with a way to model 1D objects such as contours probabilistically, in a way that led to nice, tractable computations. We now consider 2D Markov models. These are more powerful, but not as easy to compute with. In addition we will consider two additional issues. First, we will consider adding observations to our models. These observations are conditioned on the value of...

Neural Gaussian Conditional Random Fields

We propose a Conditional Random Field (CRF) model for structured regression. By constraining the feature functions as quadratic functions of outputs, the model can be conveniently represented in a Gaussian canonical form. We improved the representational power of the resulting Gaussian CRF (GCRF) model by (1) introducing an adaptive feature function that can learn nonlinear relationships betwee...

An explicit link between Gaussian fields and Gaussian Markov random fields: The SPDE approach

Continuously indexed Gaussian fields (GFs) is the most important ingredient in spatial statistical modelling and geostatistics. The specification through the covariance function gives an intuitive interpretation of the field properties. On the computational side, GFs are hampered with the big n problem, since the cost of factorising dense matrices is cubic in the dimension. Although the computa...

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...