Approximate state-space Gaussian processes via spectral transformation

Toni Karvonen, Simo Särkkä

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

5 Citations (Scopus)
211 Downloads (Pure)

Abstract

State-space representations of Gaussian process regression use Kalman filtering and smoothing theory to downscale the computational complexity of the regression in the number of data points from cubic to linear. As their exact implementation requires the covariance function to possess rational spectral density, rational approximations to the spectral density must be often used. In this article we introduce new spectral transformation based methods for this purpose: a spectral composition method and a spectral preconditioning method. We study convergence of the approximations theoretically and run numerical experiments to attest their accuracy for different densities, in particular the fractional Matern.

Original languageEnglish
Title of host publicationProceedings of the 2016 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2016
EditorsFransesco A.N. Palmieri, Aurelio Uncini, Kostas Diamantaras, Jan Larsen
Volume2016-November
ISBN (Electronic)9781509007462
DOIs
Publication statusPublished - 8 Nov 2016
MoE publication typeA4 Article in a conference publication
EventIEEE International Workshop on Machine Learning for Signal Processing - Salerno, Italy
Duration: 13 Sep 201616 Sep 2016
Conference number: 26
http://mlsp2016.conwiz.dk/home.htm

Publication series

NameIEEE International Workshop on Machine Learning for Signal Processing
PublisherIEEE COMPUTER SOCIETY PRESS
ISSN (Print)2161-0363
ISSN (Electronic)2161-0371

Workshop

WorkshopIEEE International Workshop on Machine Learning for Signal Processing
Abbreviated titleMLSP
Country/TerritoryItaly
CitySalerno
Period13/09/201616/09/2016
Internet address

Keywords

  • composite approximation
  • fractional Matérn
  • Gaussian process regression
  • spectral preconditioning
  • state-space approximation

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