Related papers: GPU-Accelerated Vecchia Approximations of Gaussian…
Recent advances in data collection technologies have led to the emergence of massive spatial datasets, with measurements obtained at millions of spatial locations. Geostatistical models typically employ Gaussian processes (GPs) to capture…
Spatial generalized linear mixed-effects models are popularly used to analyze spatially indexed univariate responses. However, with modern technology, it is common to observe vector-valued mixed-type responses, e.g., a combination of…
A Gaussian Process GP based ground segmentation method is proposed in this paper which is fully developed in a probabilistic framework. The proposed method tends to obtain a continuous realistic model of the ground. The LiDAR…
The stochastic partial differential equation approach to Gaussian processes (GPs) represents Mat\'ern GP priors in terms of $n$ finite element basis functions and Gaussian coefficients with sparse precision matrix. Such representations…
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…
Although machine learning is increasingly applied in control approaches, only few methods guarantee certifiable safety, which is necessary for real world applications. These approaches typically rely on well-understood learning algorithms,…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
Fitting a theoretical model to experimental data in a Bayesian manner using Markov chain Monte Carlo typically requires one to evaluate the model thousands (or millions) of times. When the model is a slow-to-compute physics simulation,…
In this paper, we explore the application of Gaussian Processes (GPs) for predicting mean-reverting time series with an underlying structure, using relatively unexplored functional and augmented data structures. While many conventional…
Gaussian process (GP) predictors are an important component of many Bayesian approaches to machine learning. However, even a straightforward implementation of Gaussian process regression (GPR) requires O(n^2) space and O(n^3) time for a…
This article focuses on drawing computationally-efficient predictive inference from Gaussian process (GP) regressions with a large number of features when the response is conditionally independent of the features given the projection to a…
In many areas of the observational and experimental sciences data is scarce. Data observation in high-energy astrophysics is disrupted by celestial occlusions and limited telescope time while data derived from laboratory experiments in…
Despite a large corpus of recent work on scaling up Gaussian processes, a stubborn trade-off between computational speed, prediction and uncertainty quantification accuracy, and customizability persists. This is because the vast majority of…
Standard Gaussian Process (GP) regression, a powerful machine learning tool, is computationally expensive when it is applied to large datasets, and potentially inaccurate when data points are sparsely distributed in a high-dimensional…
Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…
A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…
Gaussian processes (GPs) are flexible distributions over functions that enable high-level assumptions about unknown functions to be encoded in a parsimonious, flexible and general way. Although elegant, the application of GPs is limited by…
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…
The growing field of large-scale time domain astronomy requires methods for probabilistic data analysis that are computationally tractable, even with large datasets. Gaussian Processes are a popular class of models used for this purpose…
We present a kernel-independent method that applies hierarchical matrices to the problem of maximum likelihood estimation for Gaussian processes. The proposed approximation provides natural and scalable stochastic estimators for its…