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We consider the problem of estimating the parameters of the covariance function of a Gaussian process by cross-validation. We suggest using new cross-validation criteria derived from the literature of scoring rules. We also provide an…

Computation · Statistics 2020-08-07 Sébastien Petit , Julien Bect , Sébastien da Veiga , Paul Feliot , Emmanuel Vazquez

The problem of model selection is considered for the setting of interpolating estimators, where the number of model parameters exceeds the size of the dataset. Classical information criteria typically consider the large-data limit,…

Machine Learning · Statistics 2026-01-13 Liam Hodgkinson , Chris van der Heide , Robert Salomone , Fred Roosta , Michael W. Mahoney

This work presents a new procedure for obtaining predictive distributions in the context of Gaussian process (GP) modeling, with a relaxation of the interpolation constraints outside ranges of interest: the mean of the predictive…

Computation · Statistics 2026-01-13 Sébastien Petit , Julien Bect , Emmanuel Vazquez

Large-scale Gaussian process models are becoming increasingly important and widely used in many areas, such as, computer experiments, stochastic optimization via simulation, and machine learning using Gaussian processes. The standard…

Methodology · Statistics 2018-08-02 Yongxiang Li , Qiang Zhou , Kwok Leung Tsui , Javier Cabrera

Recent literature provides many computational and modeling approaches for covariance matrices estimation in a penalized Gaussian graphical models but relatively little study has been carried out on the choice of the tuning parameter. This…

Methodology · Statistics 2009-09-08 Heng Lian

Recommender systems are often designed based on a collaborative filtering approach, where user preferences are predicted by modelling interactions between users and items. Many common approaches to solve the collaborative filtering task are…

Machine Learning · Computer Science 2021-10-11 Yinchong Yang , Florian Buettner

Bayesian model updating based on Gaussian Process (GP) models has received attention in recent years, which incorporates kernel-based GPs to provide enhanced fidelity response predictions. Although most kernel functions provide high fitting…

Bayesian optimisation has gained great popularity as a tool for optimising the parameters of machine learning algorithms and models. Somewhat ironically, setting up the hyper-parameters of Bayesian optimisation methods is notoriously hard.…

Machine Learning · Statistics 2014-07-01 Ziyu Wang , Nando de Freitas

We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the…

Optimization and Control · Mathematics 2022-04-18 Julien Pelamatti , Rodolphe Le Riche , Céline Helbert , Christophette Blanchet-Scalliet

We propose an active set selection framework for Gaussian process classification for cases when the dataset is large enough to render its inference prohibitive. Our scheme consists of a two step alternating procedure of active set update…

Machine Learning · Statistics 2011-06-24 Ricardo Henao , Ole Winther

The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…

Numerical Analysis · Mathematics 2020-02-11 Toby Sanders , Rodrigo B. Platte , Robert D. Skeel

Gaussian process regression (GPR) is a non-parametric Bayesian technique for interpolating or fitting data. The main barrier to further uptake of this powerful tool rests in the computational costs associated with the matrices which arise…

Machine Learning · Statistics 2016-05-16 Christopher J. Moore , Alvin J. K. Chua , Christopher P. L. Berry , Jonathan R. Gair

Inferring the value of a property of a large stochastic system is a difficult task when the number of samples is insufficient to reliably estimate the probability distribution. The Bayesian estimator of the property of interest requires the…

Data Analysis, Statistics and Probability · Physics 2022-01-26 Damián G. Hernández , Inés Samengo

An interpolation error is an integral of the squared error of a regression model over a domain of interest. We consider the interpolation error for the case of misspecified Gaussian process regression: used covariance function differs from…

Statistics Theory · Mathematics 2018-03-28 A. Zaytsev , E. Romanenkova , D. Ermilov

It is argued that all model based approaches to the selection of covariates in linear regression have failed. This applies to frequentist approaches based on P-values and to Bayesian approaches although for different reasons. In the first…

Methodology · Statistics 2022-02-23 Laurie Davies

We consider the problem of estimating the mean $f$ of a Gaussian vector $Y$ with independent components of common unknown variance $\sigma^{2}$. Our estimation procedure is based on estimator selection. More precisely, we start with an…

Statistics Theory · Mathematics 2011-06-24 Yannick Baraud , Christophe Giraud , Sylvie Huet

In this paper, we introduce a novel theoretical framework for Gaussian process regression error analysis, leveraging a function-space decomposition. Based on this framework, we develop a weighted Jacobi iterative method that utilizes…

Numerical Analysis · Mathematics 2026-02-27 Tiantian Sun , Juan Zhang

With the rapid development of modern technology, massive amounts of data with complex pattern are generated. Gaussian process models that can easily fit the non-linearity in data become more and more popular nowadays. It is often the case…

Applications · Statistics 2023-09-11 Zhiyong Hu , Dipak Dey

We consider Bayesian model selection in generalized linear models that are high-dimensional, with the number of covariates p being large relative to the sample size n, but sparse in that the number of active covariates is small compared to…

Statistics Theory · Mathematics 2011-12-26 Rina Foygel , Mathias Drton

This paper presents a new variable selection approach integrated with Gaussian process (GP) regression. We consider a sparse projection of input variables and a general stationary covariance model that depends on the Euclidean distance…

Machine Learning · Computer Science 2020-08-26 Chiwoo Park , David J. Borth , Nicholas S. Wilson , Chad N. Hunter