Related papers: On the relation between Gaussian process quadratur…
Mark-point dependence plays a critical role in research problems that can be fitted into the general framework of marked point processes. In this work, we focus on adjusting for mark-point dependence when estimating the mean and covariance…
Bayesian probabilistic numerical methods for numerical integration offer significant advantages over their non-Bayesian counterparts: they can encode prior information about the integrand, and can quantify uncertainty over estimates of an…
We discuss several examples of point processes (all taken from Hough, Krishnapur, Peres, Vir\'ag (2009)) for which the autocorrelation and diffraction measures can be calculated explicitly. These include certain classes of determinantal and…
Gaussian processes occupy one of the leading places in modern statistics and probability theory due to their importance and a wealth of strong results. The common use of Gaussian processes is in connection with problems related to…
Recently, a novel linear model predictive control algorithm based on a physics-informed Gaussian Process has been introduced, whose realizations strictly follow a system of underlying linear ordinary differential equations with constant…
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…
We introduce a fast algorithm for Gaussian process regression in low dimensions, applicable to a widely-used family of non-stationary kernels. The non-stationarity of these kernels is induced by arbitrary spatially-varying vertical and…
Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this…
Bayesian cubature provides a flexible framework for numerical integration, in which a priori knowledge on the integrand can be encoded and exploited. This additional flexibility, compared to many classical cubature methods, comes at a…
This paper proposes a new formulation of functional Gaussian Process regression in manifolds, based on an Empirical Bayes approach, in the spatiotemporal random field context. We apply the machinery of tight Gaussian measures in separable…
In this work we study two Riemannian distances between infinite-dimensional positive definite Hilbert-Schmidt operators, namely affine-invariant Riemannian and Log-Hilbert-Schmidt distances, in the context of covariance operators associated…
The accuracy and effectiveness of Hermite spectral methods for the numerical discretization of partial differential equations on unbounded domains, are strongly affected by the amplitude of the Gaussian weight function employed to describe…
The techniques for polynomial interpolation and Gaussian quadrature are generalized to matrix-valued functions. It is shown how the zeros and rootvectors of matrix orthonormal polynomials can be used to get a quadrature formula with the…
This paper is considered with joint estimation of state and time-varying noise covariance matrices in non-linear stochastic state space models. We present a variational Bayes and Gaussian filtering based algorithm for efficient computation…
Multivariate generalized Gamma convolutions are distributions defined by a convolutional semi-parametric structure. Their flexible dependence structures, the marginal possibilities and their useful convolutional expression make them…
Determinantal points processes are a promising but relatively under-developed tool in machine learning and statistical modelling, being the canonical statistical example of distributions with repulsion. While their mathematical formulation…
Gaussian Processes (GPs) are widely recognized as powerful non-parametric models for regression and classification. Traditional GP frameworks predominantly operate under the assumption that the inputs are either accurately known or subject…
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 article, numerical integration is formulated as evaluation of a matrix function of a matrix that is obtained as a projection of the multiplication operator on a finite-dimensional basis. The idea is to approximate the continuous…
Gaussian processes constitute a very powerful and well-understood method for non-parametric regression and classification. In the classical framework, the training data consists of deterministic vector-valued inputs and the corresponding…