Related papers: Gaussian process hyper-parameter estimation using …

We study in this paper two classes of experimental designs, support points and projected support points, which can provide robust and effective emulation of computer experiments with Gaussian processes. These designs have two important…

A new methodology for model determination in decomposable graphical Gaussian models is developed. The Bayesian paradigm is used and, for each given graph, a hyper inverse Wishart prior distribution on the covariance matrix is considered.…

We consider maximum likelihood estimation with data from a bivariate Gaussian process with a separable exponential covariance model under fixed domain asymptotic. We first characterize the equivalence of Gaussian measures under this model.…

A multi-fidelity simulator is a numerical model, in which one of the inputs controls a trade-off between the realism and the computational cost of the simulation. Our goal is to estimate the probability of exceeding a given threshold on a…

In this work, we present a new class of models, called uncertain-input models, that allows us to treat system-identification problems in which a linear system is subject to a partially unknown input signal. To encode prior information about…

This paper deals with the construction of a metamodel (i.e. a simplified mathematical model) for a stochastic computer code (also called stochastic numerical model or stochastic simulator), where stochastic means that the code maps the…

Many real-world applications demand accurate and fast predictions, as well as reliable uncertainty estimates. However, quantifying uncertainty on high-dimensional predictions is still a severely under-investigated problem, especially when…

Model selection in Gaussian processes scales prohibitively with the size of the training dataset, both in time and memory. While many approximations exist, all incur inevitable approximation error. Recent work accounts for this error in the…

Learning uncertain dynamics models using Gaussian process~(GP) regression has been demonstrated to enable high-performance and safety-aware control strategies for challenging real-world applications. Yet, for computational tractability,…

Bayesian optimization has emerged as a highly effective tool for the safe online optimization of systems, due to its high sample efficiency and noise robustness. To further enhance its efficiency, reduced physical models of the system can…

Generating simulated training data needed for constructing sufficiently accurate surrogate models to be used for efficient optimization or parameter identification can incur a huge computational effort in the offline phase. We consider a…

Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…

The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on…

In this paper we propose the first non-parametric Bayesian model using Gaussian Processes to make inference on Poisson Point Processes without resorting to gridding the domain or to introducing latent thinning points. Unlike competing…

Gaussian Boson Sampling (GBS) have shown advantages over classical methods for performing some specific sampling tasks. To fully harness the computational power of GBS, there has been great interest in identifying their practical…

Accurate assessment of systematic uncertainties is an increasingly vital task in physics studies, where large, high-dimensional datasets, like those collected at the Large Hadron Collider, hold the key to new discoveries. Common approaches…

Gaussian process state-space models (GP-SSMs) are a very flexible family of models of nonlinear dynamical systems. They comprise a Bayesian nonparametric representation of the dynamics of the system and additional (hyper-)parameters…

Gaussian process priors are a popular choice for Bayesian analysis of regression problems. However, the implementation of these models can be complex, and ensuring that the implementation is correct can be challenging. In this paper we…

In Bayesian statistics, many problems can be expressed as the evaluation of the expectation of a quantity of interest with respect to the posterior distribution. Standard Monte Carlo method is often not applicable because the encountered…

Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…