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07/14/2023
Comparing Scale Parameter Estimators for Gaussian Process Regression: Cross Validation and Maximum Likelihood
Gaussian process (GP) regression is a Bayesian nonparametric method for ...
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10/15/2022
Multilevel Bayesian Quadrature
Multilevel Monte Carlo is a key tool for approximating integrals involvi...
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09/26/2022
Approximation in Hilbert spaces of the Gaussian and other weighted power series kernels
This article considers linear approximation based on function evaluation...
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06/17/2022
Orthonormal Expansions for Translation-Invariant Kernels
We present a general Fourier analytic technique for constructing orthono...
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03/17/2022
Maximum Likelihood Estimation in Gaussian Process Regression is Ill-Posed
Gaussian process regression underpins countless academic and industrial ...
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03/10/2022
Asymptotic Bounds for Smoothness Parameter Estimates in Gaussian Process Interpolation
It is common to model a deterministic response function, such as the out...
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01/19/2022
Error analysis for a statistical finite element method
The recently proposed statistical finite element (statFEM) approach synt...
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12/03/2021
ProbNum: Probabilistic Numerics in Python
Probabilistic numerical methods (PNMs) solve numerical problems via prob...
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10/06/2021
Estimation of the Scale Parameter for a Misspecified Gaussian Process Model
Parameters of the covariance kernel of a Gaussian process model often ne...
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06/15/2021
Black Box Probabilistic Numerics
Probabilistic numerics casts numerical tasks, such the numerical solutio...
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03/04/2021
Small Sample Spaces for Gaussian Processes
It is known that the membership in a given reproducing kernel Hilbert sp...
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02/01/2021
A Probabilistic Taylor Expansion with Applications in Filtering and Differential Equations
We study a class of Gaussian processes for which the posterior mean, for...
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04/27/2020
Integration in reproducing kernel Hilbert spaces of Gaussian kernels
The Gaussian kernel plays a central role in machine learning, uncertaint...
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04/01/2020
Sampling based approximation of linear functionals in Reproducing Kernel Hilbert Spaces
In this paper we analyze a greedy procedure to approximate a linear func...
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01/31/2020
Semi-Exact Control Functionals From Sard's Method
This paper focuses on the numerical computation of posterior expected qu...
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01/29/2020
Maximum likelihood estimation and uncertainty quantification for Gaussian process approximation of deterministic functions
Despite the ubiquity of the Gaussian process regression model, few theor...
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01/08/2020
Taylor Moment Expansion for Continuous-Discrete Gaussian Filtering and Smoothing
The paper is concerned with non-linear Gaussian filtering and smoothing ...
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12/16/2019
Kernel-based interpolation at approximate Fekete points
We construct approximate Fekete point sets for kernel-based interpolatio...
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12/20/2018
On the positivity and magnitudes of Bayesian quadrature weights
This article reviews and studies the properties of Bayesian quadrature w...
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11/28/2018
Improved Calibration of Numerical Integration Error in Sigma-Point Filters
The sigma-point filters, such as the UKF, which exploit numerical quadra...
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09/26/2018
Symmetry Exploits for Bayesian Cubature Methods
Bayesian cubature provides a flexible framework for numerical integratio...
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09/15/2018
On stability of a class of filters for non-linear stochastic systems
This article considers stability properties of a broad class of commonly...
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04/09/2018
A Bayes-Sard Cubature Method
This paper focusses on the formulation of numerical integration as an in...
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03/18/2017
Fully symmetric kernel quadrature
Kernel quadratures and other kernel-based approximation methods typicall...
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03/15/2017