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Gaussian processes (GPs) are commonly used for geospatial analysis, but they suffer from high computational complexity when dealing with massive data. For instance, the log-likelihood function required in estimating the statistical model…
Gaussian Processes (GPs) are vital for modeling and predicting irregularly-spaced, large geospatial datasets. However, their computations often pose significant challenges in large-scale applications. One popular method to approximate GPs…
Gaussian processes (GPs) are flexible, probabilistic, nonparametric models widely used in fields such as spatial statistics and machine learning. A drawback of Gaussian processes is their computational cost, with $O(N^3)$ time and $O(N^2)$…
Gaussian processes (GPs) are commonly used as models for functions, time series, and spatial fields, but they are computationally infeasible for large datasets. Focusing on the typical setting of modeling data as a GP plus an additive noise…
Gaussian processes (GPs) are highly flexible function estimators used for geospatial analysis, nonparametric regression, and machine learning, but they are computationally infeasible for large datasets. Vecchia approximations of GPs have…
The graphics processing unit (GPU) has emerged as a powerful and cost effective processor for general performance computing. GPUs are capable of an order of magnitude more floating-point operations per second as compared to modern central…
Many scientific phenomena are studied using computer experiments consisting of multiple runs of a computer model while varying the input settings. Gaussian processes (GPs) are a popular tool for the analysis of computer experiments,…
Computer models or simulators are widely used across scientific fields, but are computationally expensive limiting their use to explore possible scenarios/outcomes. Gaussian process emulators are statistical surrogates that can rapidly…
We explore how the big-three computing paradigms -- symmetric multi-processor (SMC), graphical processing units (GPUs), and cluster computing -- can together be brought to bare on large-data Gaussian processes (GP) regression problems via a…
Gaussian processes (GPs) are commonly used for prediction and inference for spatial data analyses. However, since estimation and prediction tasks have cubic time and quadratic memory complexity in number of locations, GPs are difficult to…
Latent Gaussian process (GP) models are flexible probabilistic non-parametric function models. Vecchia approximations are accurate approximations for GPs to overcome computational bottlenecks for large data, and the Laplace approximation is…
Gaussian Processes (GPs) are widely used to model dependencies in spatial statistics and machine learning. However, exact inference is computationally intractable for GP regression, with a time complexity of $O(n^3)$. The Vecchia…
Gaussian processes (GPs) are a widely used regression tool, but the cubic complexity of exact solvers limits their scalability. To address this challenge, we extend the GPRat library by incorporating a fully GPU-resident GP prediction…
Generalized Gaussian processes (GGPs) are highly flexible models that combine latent GPs with potentially non-Gaussian likelihoods from the exponential family. GGPs can be used in a variety of settings, including GP classification,…
In this work, we present an extension of Gaussian process (GP) models with sophisticated parallelization and GPU acceleration. The parallelization scheme arises naturally from the modular computational structure w.r.t. datapoints in the…
Model selection in Gaussian processes scales prohibitively with the size of the training dataset, both in time and memory. While many approximations exist, all incur inevitable approximation error. Recent work accounts for this error in the…
Deep Gaussian processes (DGPs) upgrade ordinary GPs through functional composition, in which intermediate GP layers warp the original inputs, providing flexibility to model non-stationary dynamics. Two DGP regimes have emerged in recent…
Gaussian processes are flexible, probabilistic, non-parametric models widely used in machine learning and statistics. However, their scalability to large data sets is limited by computational constraints. To overcome these challenges, we…
Emulating computationally intensive scientific simulations is crucial for enabling uncertainty quantification, optimization, and informed decision-making at scale. Gaussian Processes (GPs) offer a flexible and data-efficient foundation for…
Gaussian process (GP) regression is a flexible, nonparametric approach to regression that naturally quantifies uncertainty. In many applications, the number of responses and covariates are both large, and a goal is to select covariates that…