Related papers: Estimation and model errors in Gaussian-process-ba…
Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of…
Linear systems occur throughout engineering and the sciences, most notably as differential equations. In many cases the forcing function for the system is unknown, and interest lies in using noisy observations of the system to infer the…
Gaussian processes (GPs) offer a flexible class of priors for nonparametric Bayesian regression, but popular GP posterior inference methods are typically prohibitively slow or lack desirable finite-data guarantees on quality. We develop an…
The accurate prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the variances. Moreover, function…
The Gaussian process (GP) regression model is a widely employed surrogate modeling technique for computer experiments, offering precise predictions and statistical inference for the computer simulators that generate experimental data.…
The presence of uncertainties are inevitable in engineering design and analysis, where failure in understanding their effects might lead to the structural or functional failure of the systems. The role of global sensitivity analysis in this…
In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…
Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…
We propose an algorithm for an optimal adaptive selection of points from the design domain of input random variables that are needed for an accurate estimation of failure probability and the determination of the boundary between safe and…
Global sensitivity analysis (GSA) quantifies the influence of uncertain variables in a mathematical model. The Sobol' indices, a commonly used tool in GSA, seek to do this by attributing to each variable its relative contribution to the…
In this paper we consider the problem of Gaussian process classifier (GPC) model selection with different Leave-One-Out (LOO) Cross Validation (CV) based optimization criteria and provide a practical algorithm using LOO predictive…
This paper presents a method for approximate Gaussian process (GP) regression with tensor networks (TNs). A parametric approximation of a GP uses a linear combination of basis functions, where the accuracy of the approximation depends on…
Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization, $\ell_1$ norm regularized optimization, and $\ell_0$ norm regularized…
Basis Function (BF) expansions are a cornerstone of any engineer's toolbox for computational function approximation which shares connections with both neural networks and Gaussian processes. Even though BF expansions are an intuitive and…
This paper investigates the iterates $\hbb^1,\dots,\hbb^T$ obtained from iterative algorithms in high-dimensional linear regression problems, in the regime where the feature dimension $p$ is comparable with the sample size $n$, i.e., $p…
We propose to estimate a metamodel and the sensitivity indices of a complex model m in the Gaussian regression framework. Our approach combines methods for sensitivity analysis of complex models and statistical tools for sparse…
Stochastic kinetic models are ubiquitous in physics, yet inferring their parameters from experimental data remains challenging. In deterministic models, parameter inference often relies on gradients, as they can be obtained efficiently…
An energy efficient use of large scale sensor networks necessitates activating a subset of possible sensors for estimation at a fusion center. The problem is inherently combinatorial; to this end, a set of iterative, randomized algorithms…
We consider the problem of learning the level set for which a noisy black-box function exceeds a given threshold. To efficiently reconstruct the level set, we investigate Gaussian process (GP) metamodels. Our focus is on strongly stochastic…
We study Gaussian Process Thompson Sampling (GP-TS) for sequential decision-making over compact, continuous action spaces and provide a frequentist regret analysis based on fractional Gaussian process posteriors, without relying on domain…