Bayesian probabilistic numerical methods
Over forty years ago average-case error was proposed in the applied mathematics literature
as an alternative criterion with which to assess numerical methods. In contrast to worst-case …
as an alternative criterion with which to assess numerical methods. In contrast to worst-case …
Probabilistic integration
A research frontier has emerged in scientific computation, wherein discretisation error is
regarded as a source of epistemic uncertainty that can be modelled. This raises several …
regarded as a source of epistemic uncertainty that can be modelled. This raises several …
A modern retrospective on probabilistic numerics
CJ Oates, TJ Sullivan - Statistics and computing, 2019 - Springer
This article attempts to place the emergence of probabilistic numerics as a mathematical–
statistical research field within its historical context and to explore how its gradual …
statistical research field within its historical context and to explore how its gradual …
Convergence guarantees for Gaussian process means with misspecified likelihoods and smoothness
Gaussian processes are ubiquitous in machine learning, statistics, and applied
mathematics. They provide a exible modelling framework for approximating functions, whilst …
mathematics. They provide a exible modelling framework for approximating functions, whilst …
Meta-learning control variates: Variance reduction with limited data
Control variates can be a powerful tool to reduce the variance of Monte Carlo estimators, but
constructing effective control variates can be challenging when the number of samples is …
constructing effective control variates can be challenging when the number of samples is …
Fast and robust shortest paths on manifolds learned from data
We propose a fast, simple and robust algorithm for computing shortest paths and distances
on Riemannian manifolds learned from data. This amounts to solving a system of ordinary …
on Riemannian manifolds learned from data. This amounts to solving a system of ordinary …
Convergence rates of Gaussian ODE filters
A recently introduced class of probabilistic (uncertainty-aware) solvers for ordinary
differential equations (ODEs) applies Gaussian (Kalman) filtering to initial value problems …
differential equations (ODEs) applies Gaussian (Kalman) filtering to initial value problems …
Baysian numerical integration with neural networks
Bayesian probabilistic numerical methods for numerical integration offer significant
advantages over their non-Bayesian counterparts: they can encode prior information about …
advantages over their non-Bayesian counterparts: they can encode prior information about …
Convergence guarantees for adaptive Bayesian quadrature methods
M Kanagawa, P Hennig - Advances in neural information …, 2019 - proceedings.neurips.cc
Adaptive Bayesian quadrature (ABQ) is a powerful approach to numerical integration that
empirically compares favorably with Monte Carlo integration on problems of medium …
empirically compares favorably with Monte Carlo integration on problems of medium …
Active multi-information source Bayesian quadrature
A Gessner, J Gonzalez… - Uncertainty in Artificial …, 2020 - proceedings.mlr.press
Bayesian quadrature (BQ) is a sample-efficient probabilistic numerical method to solve
integrals of expensive-to-evaluate black-box functions, yet so far, active BQ learning …
integrals of expensive-to-evaluate black-box functions, yet so far, active BQ learning …