A probabilistic Taylor expansion with applications in filtering and differential equations
A probabilistic Taylor expansion with applications in filtering and differential equations
We study a class of Gaussian processes for which the posterior mean, for a particular choice of data, replicates a truncated Taylor expansion of any order. The data consists of derivative evaluations at the expansion point and the prior covariance kernel belongs to the class of Taylor kernels, which can be written in a certain power series form. This permits statistical modelling of the uncertainty in a variety of algorithms that exploit first and second order Taylor expansions. To demonstrate the utility of this Gaussian process model we introduce new probabilistic versions of the classical extended Kalman filter for non-linear state estimation and the Euler method for solving ordinary differential equations.
Karvonen, Toni
bb48042f-45d1-4f44-841b-0817f45961d8
Cockayne, Jon
da87c8b2-fafb-4856-938d-50be8f0e4a5b
Tronarp, Filip
e51d70a4-6cec-4bd9-b065-142c180e2439
Sarkka, Simo
5402acd1-808a-4428-8900-adcac00b709a
Karvonen, Toni
bb48042f-45d1-4f44-841b-0817f45961d8
Cockayne, Jon
da87c8b2-fafb-4856-938d-50be8f0e4a5b
Tronarp, Filip
e51d70a4-6cec-4bd9-b065-142c180e2439
Sarkka, Simo
5402acd1-808a-4428-8900-adcac00b709a
Karvonen, Toni, Cockayne, Jon, Tronarp, Filip and Sarkka, Simo
(2021)
A probabilistic Taylor expansion with applications in filtering and differential equations.
TMLR: Transactions on Machine Learning Research.
(In Press)
Abstract
We study a class of Gaussian processes for which the posterior mean, for a particular choice of data, replicates a truncated Taylor expansion of any order. The data consists of derivative evaluations at the expansion point and the prior covariance kernel belongs to the class of Taylor kernels, which can be written in a certain power series form. This permits statistical modelling of the uncertainty in a variety of algorithms that exploit first and second order Taylor expansions. To demonstrate the utility of this Gaussian process model we introduce new probabilistic versions of the classical extended Kalman filter for non-linear state estimation and the Euler method for solving ordinary differential equations.
Text
A Probabilistic Taylor Expansion with Applications in Filtering and Differential Equations
- Accepted Manuscript
Restricted to Repository staff only
Request a copy
More information
Accepted/In Press date: 1 February 2021
Identifiers
Local EPrints ID: 451486
URI: http://eprints.soton.ac.uk/id/eprint/451486
PURE UUID: b533e351-0468-4c0c-aee1-2f1f79019a6b
Catalogue record
Date deposited: 30 Sep 2021 16:34
Last modified: 06 Nov 2024 03:04
Export record
Contributors
Author:
Toni Karvonen
Author:
Filip Tronarp
Author:
Simo Sarkka
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics
