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 parallelizeable approximation to the full GP marginal likelihood, enabling latent variable modeling and hyperparameter selection on large datasets. We demonstrate its effectiveness on synthetic spatial data as well as a real-world application to seismic event location.
Code (1)
Tasks
BIG-bench Machine LearningGaussian ProcessesMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Invariances of random fields paths, with applications in Gaussian Process Regression
We study pathwise invariances of centred random fields that can be controlled through the covariance. A result involving composition operators is obtained in second-order settings, and we show that various path propertie…
regressionScalable Parallel Factorizations of SDD Matrices and Efficient Sampling for Gaussian Graphical Models
Motivated by a sampling problem basic to computational statistical inference, we develop a nearly optimal algorithm for a fundamental problem in spectral graph theory and numerical analysis. Given an $n\times n$ SDDM mat…
Efficient methods for Gaussian Markov random fields under sparse linear constraints
Methods for inference and simulation of linearly constrained Gaussian Markov Random Fields (GMRF) are computationally prohibitive when the number of constraints is large. In some cases, such as for intrinsic GMRFs, they …
Local, algebraic simplifications of Gaussian random fields
Many applications of Gaussian random fields and Gaussian random processes are limited by the computational complexity of evaluating the probability density function, which involves inverting the relevant covariance matri…
On the Kullback-Leibler divergence between pairwise isotropic Gaussian-Markov random fields
The Kullback-Leibler divergence or relative entropy is an information-theoretic measure between statistical models that play an important role in measuring a distance between random variables. In the study of complex sys…
DenoisingImage DenoisingMetric Learning