Mitigating spatial confounding by explicitly correlating Gaussian random fields

Transformed Gaussian Markov Random Fields and 1 Spatial Modeling

15 The Gaussian random field (GRF) and the Gaussian Markov random field (GMRF) have 16 been widely used to accommodate spatial dependence under the generalized linear mixed 17 model framework. These models have limitations rooted in the symmetry and thin tail of the 18 Gaussian distribution. We introduce a new class of random fields, termed transformed GRF 19 (TGRF), and a new class of Markov r...

Skew-Gaussian Random Fields

Skewness is often present in a wide range of spatial prediction problems, and modeling it in the spatial context remains a challenging problem. In this study a skew-Gaussian random field is considered. The skew-Gaussian random field is constructed by using the multivariate closed skew-normal distribution, which is a generalization of the traditional normal distribution. We present an Metropolis...

Gaussian Process Random Fields

Gaussian processes have been successful in both supervised and unsupervised machine learning tasks, but their computational complexity has constrained practical applications. We introduce a new approximation for large-scale Gaussian processes, the Gaussian Process Random Field (GPRF), in which local GPs are coupled via pairwise potentials. The GPRF likelihood is a simple, tractable, and paralle...

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...

Singularities in Gaussian Random Fields