Related papers: Fast Bayesian inference of Block Nearest Neighbor …

Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations become large. This manuscript develops a class of highly scalable Nearest Neighbor Gaussian Process…

Gaussian processes (GPs) are instrumental in modeling spatial processes, offering precise interpolation and prediction capabilities across fields such as environmental science and biology. Recently, there has been growing interest in…

Gaussian processes are ubiquitous as the primary tool for modeling spatial data. However, the Gaussian process is limited by its $\mathcal{O}(n^3)$ cost, making direct parameter fitting algorithms infeasible for the scale of modern data…

We consider alternate formulations of recently proposed hierarchical Nearest Neighbor Gaussian Process (NNGP) models (Datta et al., 2016a) for improved convergence, faster computing time, and more robust and reproducible Bayesian inference.…

A key challenge in spatial statistics is the analysis for massive spatially-referenced data sets. Such analyses often proceed from Gaussian process specifications that can produce rich and robust inference, but involve dense covariance…

Variational approximations to Gaussian processes (GPs) typically use a small set of inducing points to form a low-rank approximation to the covariance matrix. In this work, we instead exploit a sparse approximation of the precision matrix.…

Obtaining accurate water level predictions are essential for water resource management and implementing flood mitigation strategies. Several data-driven models can be found in the literature. However, there has been limited research with…

Gaussian Processes (GP) is a staple in the toolkit of a spatial statistician. Well-documented computing roadblocks in the analysis of large geospatial datasets using Gaussian Processes have now been successfully mitigated via several recent…

This paper describes and illustrates functionality of the spNNGP R package. The package provides a suite of spatial regression models for Gaussian and non-Gaussian point-referenced outcomes that are spatially indexed. The package implements…

Gaussian process ($GP$) regression is a widely used non-parametric modeling tool, but its cubic complexity in the training size limits its use on massive data sets. A practical remedy is to predict using only the nearest neighbours of each…

We propose a nested Gaussian process (nGP) as a locally adaptive prior for Bayesian nonparametric regression. Specified through a set of stochastic differential equations (SDEs), the nGP imposes a Gaussian process prior for the function's…

In spite of the diverse literature on nonstationary spatial modeling and approximate Gaussian process (GP) methods, there are no general approaches for conducting fully Bayesian inference for moderately sized nonstationary spatial data sets…

Even though Nearest Neighbor Gaussian Processes (NNGP) alleviate considerably MCMC implementation of Bayesian space-time models, they do not solve the convergence problems caused by high model dimension. Frugal alternatives such as response…

With the growing capabilities of Geographic Information Systems (GIS) and user-friendly software, statisticians today routinely encounter geographically referenced data containing observations from a large number of spatial locations and…

The rapid growth of earth observation systems calls for a scalable approach to interpolate remote-sensing observations. These methods in principle, should acquire more information about the observed field as data grows. Gaussian processes…

We introduce a flexible and scalable class of Bayesian geostatistical models for discrete data, based on the class of nearest neighbor mixture transition distribution processes (NNMP), referred to as discrete NNMP. The proposed class…

We provide simple schemes to build Bayesian Neural Networks (BNNs), block by block, inspired by a recent idea of computation skeletons. We show how by adjusting the types of blocks that are used within the computation skeleton, we can…

Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…

Approximations to Gaussian processes based on inducing variables, combined with variational inference techniques, enable state-of-the-art sparse approaches to infer GPs at scale through mini batch-based learning. In this work, we address…

Gaussian Process (GP) Variational Autoencoders (VAEs) extend standard VAEs by replacing the fully factorised Gaussian prior with a GP prior, thereby capturing richer correlations among latent variables. However, performing exact GP…