相关论文: Gaussian Process Kernels for Popular State-Space T…

Gaussian Processes (GPs) are powerful non-parametric Bayesian models for regression of scalar fields, formulated under the assumption that measurement locations are perfectly known and the corresponding field measurements have Gaussian…

Grid-based modelling is widely used for estimating stellar parameters. However, stellar model grid is sparse because of the computational cost. This paper demonstrates an application of a machine-learning algorithm using the Gaussian…

Gaussian process state-space model (GPSSM) is a fully probabilistic state-space model that has attracted much attention over the past decade. However, the outputs of the transition function in the existing GPSSMs are assumed to be…

Gaussian processes provide a flexible framework for forecasting, removing noise, and interpreting long temporal datasets. State space modelling (Kalman filtering) enables these non-parametric models to be deployed on long datasets by…

Applying Gaussian processes (GPs) to very large datasets remains a challenge due to limited computational scalability. Matrix structures, such as the Kronecker product, can accelerate operations significantly, but their application commonly…

Gaussian process (GP) is a powerful modeling method with applications in machine learning for various engineering and non-engineering fields. Despite numerous benefits of modeling using GPs, the computational complexity associated with GPs…

A Gaussian Process (GP) is a prominent mathematical framework for stochastic function approximation in science and engineering applications. This success is largely attributed to the GP's analytical tractability, robustness, non-parametric…

Computational models of complex physical systems often rely on simplifying assumptions which inevitably introduce model error, with consequent predictive errors. Given data on model observables, the estimation of parameterized model-error…

Gaussian process (GP) models are widely used to analyze spatially referenced data and to predict values at locations without observations. In contrast to many algorithmic procedures, GP models are based on a statistical framework, which…

We propose a representation of Gaussian processes (GPs) based on powers of the integral operator defined by a kernel function, we call these stochastic processes integral Gaussian processes (IGPs). Sample paths from IGPs are functions…

We apply Gaussian process (GP) regression, which provides a powerful non-parametric probabilistic method of relating inputs to outputs, to survival data consisting of time-to-event and covariate measurements. In this context, the covariates…

Motivated by questions in quantum theory, we study Hilbert space valued Gaussian processes, and operator-valued kernels, i.e., kernels taking values in B(H) (= all bounded linear operators in a fixed Hilbert space H). We begin with a…

Gaussian processes (GPs) are important models in supervised machine learning. Training in Gaussian processes refers to selecting the covariance functions and the associated parameters in order to improve the outcome of predictions, the core…

In this paper, we revisit batch state estimation through the lens of Gaussian process (GP) regression. We consider continuous-discrete estimation problems wherein a trajectory is viewed as a one-dimensional GP, with time as the independent…

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…

We provide a survey of nonstationary surrogate models which utilize Gaussian processes (GPs) or variations thereof, including nonstationary kernel adaptations, partition and local GPs, and spatial warpings through deep Gaussian processes.…

It has long been known that a single-layer fully-connected neural network with an i.i.d. prior over its parameters is equivalent to a Gaussian process (GP), in the limit of infinite network width. This correspondence enables exact Bayesian…

We propose a parallelizable sparse inverse formulation Gaussian process (SpInGP) for temporal models. It uses a sparse precision GP formulation and sparse matrix routines to speed up the computations. Due to the state-space formulation used…

We investigate uncertainties in the estimation of the Hubble constant ($H_0$) arising from Gaussian Process (GP) reconstruction, demonstrating that the choice of kernel introduces systematic variations comparable to those arising from…

We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data.…