Hilbert-Space Reduced-Rank Methods for Deep Gaussian Processes

Muhammad F. Emzir, Sari Lasanen, Zenith Purisha, Simo Särkkä

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

2 Citations (Scopus)

Abstract

A deep Gaussian process is a hierarchy of Gaussian processes where the process at each level is Gaussian given the process on the next level. In this paper, we recast special deep Gaussian processes as solutions of stochastic partial differential equations (SPDEs). Each of these SPDEs has parameters which are functions of the solutions to other SPDEs. To avoid solving SPDEs explicitly, we transform the SPDEs to finite-dimensional objects by truncating the underlying Hilbert space expansion. We then use a Markov chain Monte Carlo technique designed for function spaces to sample its posterior distribution. For a one-dimensional signal example, we show that the regression can offer discontinuity detection and smoothness constraints, which are competing with each other.

Original languageEnglish
Title of host publicationProceedings of the 29th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2019
ISBN (Electronic)9781728108247
DOIs
Publication statusPublished - 1 Oct 2019
MoE publication typeA4 Article in a conference publication
EventIEEE International Workshop on Machine Learning for Signal Processing - Pittsburgh, United States
Duration: 13 Oct 201916 Oct 2019
Conference number: 29

Publication series

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

Workshop

WorkshopIEEE International Workshop on Machine Learning for Signal Processing
Abbreviated titleMLSP
Country/TerritoryUnited States
CityPittsburgh
Period13/10/201916/10/2019

Keywords

  • Bayesian inference
  • Deep Gaussian processes
  • Gaussian process
  • Markov chain Monte Carlo

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