Related papers: Gaussian Processes with Input Location Error and A…

We address the issue of knots selection for Gaussian predictive process methodology. Predictive process approximation provides an effective solution to the cubic order computational complexity of Gaussian process models. This approximation…

In this paper, we study the prediction of a circularly symmetric zero-mean stationary Gaussian process from a window of observations consisting of finitely many samples. This is a prevalent problem in a wide range of applications in…

This work falls within the context of predicting the value of a real function at some input locations given a limited number of observations of this function. The Kriging interpolation technique (or Gaussian process regression) is often…

We consider the estimation of a sparse parameter vector from measurements corrupted by white Gaussian noise. Our focus is on unbiased estimation as a setting under which the difficulty of the problem can be quantified analytically. We show…

The objective of this work is to quantify the reconstruction error in sparse inverse problems with measures and stochastic noise, motivated by optimal sensor placement. To be useful in this context, the error quantities must be explicit in…

In the Big Data era, with the ubiquity of geolocation sensors in particular, massive datasets exhibiting a possibly complex spatial dependence structure are becoming increasingly available. In this context, the standard probabilistic theory…

We provide a new kriging procedure of processes on graphs. Based on the construction of Gaussian random processes indexed by graphs, we extend to this framework the usual linear prediction method for spatial random fields, known as kriging.…

Gaussian processes are frequently deployed as part of larger machine learning and decision-making systems, for instance in geospatial modeling, Bayesian optimization, or in latent Gaussian models. Within a system, the Gaussian process model…

Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…

Signal processing in non-Gaussian noise environment is addressed in this paper. For many real-life situations, the additive noise process present in the system is found to be dominantly non-Gaussian. The problem of detection and estimation…

This paper considers the quantification of the prediction performance in Gaussian process regression. The standard approach is to base the prediction error bars on the theoretical predictive variance, which is a lower bound on the mean…

Real-world measurement noise in applications like robotics is often correlated in time, but we typically assume i.i.d. Gaussian noise for filtering. We propose general Gaussian Processes as a non-parametric model for correlated measurement…

Gaussian processes (GPs) are a ubiquitous tool for geostatistical modeling with high levels of flexibility and interpretability, and the ability to make predictions at unseen spatial locations through a process called Kriging. Estimation of…

We study the problem of recovering Gaussian data under adversarial corruptions when the noises are low-rank and the corruptions are on the coordinate level. Concretely, we assume that the Gaussian noises lie in an unknown $k$-dimensional…

This paper is centered around the approximation of dynamical systems by means of Gaussian processes. To this end, trajectories of such systems must be collected to be used as training data. The measurements of these trajectories are…

Gaussian process modeling is a standard tool for building emulators for computer experiments, which are usually used to study deterministic functions, for example, a solution to a given system of partial differential equations. This work…

Noise is an unavoidable part of most measurements which can hinder a correct interpretation of the data. Uncertainties propagate in the data analysis and can lead to biased results even in basic descriptive statistics such as the central…

In this work, we propose a new Gaussian process regression (GPR) method: physics information aided Kriging (PhIK). In the standard data-driven Kriging, the unknown function of interest is usually treated as a Gaussian process with assumed…

Spatial prediction requires expensive computation to invert the spatial covariance matrix it depends on and also has considerable storage needs. This work concentrates on computationally efficient algorithms for prediction using very large…

We address the problem of uncertainty quantification (UQ) in the localization of a sound source within adverse acoustic environments. Estimating the position of the source is influenced by various factors, such as noise and reverberation,…