相关论文: regTPS-KLE: A Novel Approach To Approximate A Gaus…

We introduce a new scalable approximation for Gaussian processes with provable guarantees which hold simultaneously over its entire parameter space. Our approximation is obtained from an improved sample complexity analysis for sparse…

We consider the problem of selecting covariates in spatial linear models with Gaussian process errors. Penalized maximum likelihood estimation (PMLE) that enables simultaneous variable selection and parameter estimation is developed and,…

Gaussian Process regression is a kernel method successfully adopted in many real-life applications. Recently, there is a growing interest on extending this method to non-Euclidean input spaces, like the one considered in this paper,…

We study the nonparametric covariance estimation of a stationary Gaussian field X observed on a regular lattice. In the time series setting, some procedures like AIC are proved to achieve optimal model selection among autoregressive models.…

Variational Bayesian inference is an important machine-learning tool that finds application from statistics to robotics. The goal is to find an approximate probability density function (PDF) from a chosen family that is in some sense…

Computer models are used as replacements for physical experiments in a large variety of applications. Nevertheless, direct use of the computer model for the ultimate scientific objective is often limited by the complexity and cost of the…

Gaussian Process (GP) regression is a powerful nonparametric Bayesian framework, but its performance depends critically on the choice of covariance kernel. Selecting an appropriate kernel is therefore central to model quality, yet remains…

Both in terrestrial and extraterrestrial environments, the precise and informative model of the ground and the surface ahead is crucial for navigation and obstacle avoidance. The ground surface is not always flat and it may be sloped, bumpy…

Spatial-temporal Gaussian process regression is a popular method for spatial-temporal data modeling. Its state-of-art implementation is based on the state-space model realization of the spatial-temporal Gaussian process and its…

We propose a new approach for the modeling large datasets of nonstationary spatial processes that combines a latent low rank process and a sparse covariance model. The low rank component coefficients are endowed with a flexible graphical…

Several emerging post-Bayesian methods target a probability distribution for which an entropy-regularised variational objective is minimised. This increased flexibility introduces a computational challenge, as one loses access to an…

In this work we study the non-parametric reconstruction of spatio-temporal dynamical Gaussian processes (GPs) via GP regression from sparse and noisy data. GPs have been mainly applied to spatial regression where they represent one of the…

A central challenge in Bayesian inference is efficiently approximating posterior distributions. Stein Variational Gradient Descent (SVGD) is a popular variational inference method which transports a set of particles to approximate a target…

Gaussian processes are powerful non-parametric probabilistic models for stochastic functions. However, the direct implementation entails a complexity that is computationally intractable when the number of observations is large, especially…

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…

Skew-symmetric functions are a class of functions defined on a product space $M \times M$ that are antisymmetric with respect to the order of their inputs. In [13], the authors proved that non-deterministic skew-symmetric Gaussian fields…

This work considers the computation of risk measures for quantities of interest governed by PDEs with Gaussian random field parameters using Taylor approximations. While efficient, Taylor approximations are local to the point of expansion,…

Many physical and mathematical models involve random fields in their input data. Examples are ordinary differential equations, partial differential equations and integro--differential equations with uncertainties in the coefficient…

This paper investigates the approximation of Gaussian random variables in Banach spaces, focusing on the high-probability bounds for the approximation of Gaussian random variables using finitely many observations. We derive non-asymptotic…

Generative models and those with computationally intractable likelihoods are widely used to describe complex systems in the natural sciences, social sciences, and engineering. Fitting these models to data requires likelihood-free inference…