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We discuss the correspondence between Gaussian process regression and Geometric Harmonics, two similar kernel-based methods that are typically used in different contexts. Research communities surrounding the two concepts often pursue…
Some scenarios require the computation of a predictive distribution of a new value evaluated on an objective function conditioned on previous observations. We are interested on using a model that makes valid assumptions on the objective…
Linear filtering problem for infinite-dimensional Gaussian processes is studied, the observation process being finite-dimensional. Integral equations for the filter and for covariance of the error are derived. General results are applied to…
Importance sampling (IS) and numerical integration methods are usually employed for approximating moments of complicated target distributions. In its basic procedure, the IS methodology randomly draws samples from a proposal distribution…
Recently nonparametric functional model with functional responses has been proposed within the functional reproducing kernel Hilbert spaces (fRKHS) framework. Motivated by its superior performance and also its limitations, we propose a…
A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…
In the context of Gaussian conditioning, greedy algorithms iteratively select the most informative measurements, given an observed Gaussian random variable. However, the convergence analysis for conditioning Gaussian random variables…
In this review, the state-of-the-art for goodness-of-fit testing for spatial point processes is summarized. Test statistics based on classical functional summary statistics and recent contributions from topological data analysis are…
This paper investigates the mean square error optimal estimation of scale invariant Wigner spectrum for the class of Gaussian locally self-similar processes, by the multitaper method. In this method, the spectrum is estimated as a weighted…
Gaussian processes are powerful non-parametric probabilistic models for stochastic functions. However, the direct implementation entails a complexity that is computationally intractable when the number of observations is large, especially…
The symplectic eigenvalues play a significant role in finite mode quantum information theory, and Williamson normal form proves to be a valuable tool in this area. Understanding the symplectic spectrum of a Gaussian Covariance Operator is a…
In this paper, we consider the problem of approximating the spectral distribution for a class of random operators over sofic groups. For this purpose, we make use of the concept of locally and empirically converging measures defined by…
Motivated by practical applications, I present a novel and comprehensive framework for operator-valued positive definite kernels. This framework is applied to both operator theory and stochastic processes. The first application focuses on…
In this work, we investigate Gaussian process regression used to recover a function based on noisy observations. We derive upper and lower error bounds for Gaussian process regression with possibly misspecified correlation functions. The…
The scope of this text is to study a process that induces another proof of the Spectral Embedding Theorem: that any densely defined symmetric operator can be extended by a multiplication operator through an embedding of the Hilbert space…
A method to perform unfolding with Gaussian processes (GPs) is presented. Using Bayesian regression, we define an estimator for the underlying truth distribution as the mode of the posterior. We show that in the case where the bin contents…
Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation,…
This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and…
Pairs of equivalent Gaussian distributions for centered stationary processes on homogeneous spaces can be characterized in terms of their spectral measures. The purpose of this note is to consider part of the latter characterization from…
We develop a scalable class of models for latent variable estimation using composite Gaussian processes, with a focus on derivative Gaussian processes. We jointly model multiple data sources as outputs to improve the accuracy of latent…