Related papers: Efficient methods for Gaussian Markov random field…

Gaussian fields (GFs) are frequently used in spatial statistics for their versatility. The associated computational cost can be a bottleneck, especially in realistic applications. It has been shown that computational efficiency can be…

Gaussian Markov random fields (GMRFs) are useful in a broad range of applications. In this paper we tackle the problem of learning a sparse GMRF in a high-dimensional space. Our approach uses the l1-norm as a regularization on the inverse…

In this paper a new approach for constructing \emph{multivariate} Gaussian random fields (GRFs) using systems of stochastic partial differential equations (SPDEs) has been introduced and applied to simulated data and real data. By solving a…

Sampling from Gaussian Markov random fields (GMRFs), that is multivariate Gaussian ran- dom vectors that are parameterised by the inverse of their covariance matrix, is a fundamental problem in computational statistics. In this paper, we…

Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources. As part of a broader effort in scientific machine learning, many recent works have incorporated physical constraints or other a…

Gaussian Markov random fields are used in a large number of disciplines in machine vision and spatial statistics. The models take advantage of sparsity in matrices introduced through the Markov assumptions, and all operations in inference…

Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…

In this paper, we study the problem of inferring time-varying Markov random fields (MRF), where the underlying graphical model is both sparse and changes sparsely over time. Most of the existing methods for the inference of time-varying…

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…

Machine learning methods on graphs have proven useful in many applications due to their ability to handle generally structured data. The framework of Gaussian Markov Random Fields (GMRFs) provides a principled way to define Gaussian models…

This paper presents an approach for constrained Gaussian Process (GP) regression where we assume that a set of linear transformations of the process are bounded. It is motivated by machine learning applications for high-consequence…

We present a new method for estimating multivariate, second-order stationary Gaussian Random Field (GRF) models based on the Sparse Precision matrix Selection (SPS) algorithm, proposed by Davanloo et al. (2015) for estimating scalar GRF…

Gaussian Markov random fields (GMRFs) are popular for modeling dependence in large areal datasets due to their ease of interpretation and computational convenience afforded by the sparse precision matrices needed for random variable…

Learning a Gaussian Mixture Model (GMM) is hard when the number of parameters is too large given the amount of available data. As a remedy, we propose restricting the GMM to a Gaussian Markov Random Field Mixture Model (GMRF-MM), as well as…

Probabilistic inference in high-dimensional state-space models is computationally challenging. For many spatiotemporal systems, however, prior knowledge about the dependency structure of state variables is available. We leverage this…

The computational cost for inference and prediction of statistical models based on Gaussian processes with Mat\'ern covariance functions scales cubicly with the number of observations, limiting their applicability to large data sets. The…

The Gaussian random field (GRF) and the Gaussian Markov random field (GMRF) have been widely used to accommodate spatial dependence under the generalized linear mixed model framework. These models have limitations rooted in the symmetry and…

We propose an efficient optimization algorithm for selecting a subset of training data to induce sparsity for Gaussian process regression. The algorithm estimates an inducing set and the hyperparameters using a single objective, either the…

In this paper we propose a new approach for constructing \emph{multivariate} Gaussian random fields (GRFs) with oscillating covariance functions through systems of stochastic partial differential equations (SPDEs). We discuss how to build…

Nonparametric regression for massive numbers of samples (n) and features (p) is an increasingly important problem. In big n settings, a common strategy is to partition the feature space, and then separately apply simple models to each…