Hilbert-Space Reduced-Rank Methods for Deep Gaussian Processes

Muhammad F. Emzir; Sari Lasanen; Zenith Purisha; Simo Sarkka

doi:10.1109/MLSP.2019.8918874

Hilbert-Space Reduced-Rank Methods for Deep Gaussian Processes

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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

5 Scopus citations

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 language	English
Title of host publication	2019 IEEE 29th International Workshop on Machine Learning for Signal Processing, MLSP 2019
Publisher	IEEE Computer Society
ISBN (Electronic)	9781728108247
DOIs	https://doi.org/10.1109/MLSP.2019.8918874
State	Published - Oct 2019
Externally published	Yes

Publication series

Name	IEEE International Workshop on Machine Learning for Signal Processing, MLSP
Volume	2019-October
ISSN (Print)	2161-0363
ISSN (Electronic)	2161-0371

Bibliographical note

Publisher Copyright:
© 2019 IEEE.

Keywords

Bayesian inference
Deep Gaussian processes
Gaussian process
Markov chain Monte Carlo

ASJC Scopus subject areas

Human-Computer Interaction
Signal Processing

Access to Document

10.1109/MLSP.2019.8918874

Cite this

Emzir, M. F., Lasanen, S., Purisha, Z., & Sarkka, S. (2019). Hilbert-Space Reduced-Rank Methods for Deep Gaussian Processes. In 2019 IEEE 29th International Workshop on Machine Learning for Signal Processing, MLSP 2019 Article 8918874 (IEEE International Workshop on Machine Learning for Signal Processing, MLSP; Vol. 2019-October). IEEE Computer Society. https://doi.org/10.1109/MLSP.2019.8918874

@inproceedings{f8561be3a3164873af1da5802af42441,

title = "Hilbert-Space Reduced-Rank Methods for Deep Gaussian Processes",

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.",

keywords = "Bayesian inference, Deep Gaussian processes, Gaussian process, Markov chain Monte Carlo",

author = "Emzir, \{Muhammad F.\} and Sari Lasanen and Zenith Purisha and Simo Sarkka",

note = "Publisher Copyright: {\textcopyright} 2019 IEEE.",

year = "2019",

month = oct,

doi = "10.1109/MLSP.2019.8918874",

language = "English",

series = "IEEE International Workshop on Machine Learning for Signal Processing, MLSP",

publisher = "IEEE Computer Society",

booktitle = "2019 IEEE 29th International Workshop on Machine Learning for Signal Processing, MLSP 2019",

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}

Emzir, MF, Lasanen, S, Purisha, Z & Sarkka, S 2019, Hilbert-Space Reduced-Rank Methods for Deep Gaussian Processes. in 2019 IEEE 29th International Workshop on Machine Learning for Signal Processing, MLSP 2019., 8918874, IEEE International Workshop on Machine Learning for Signal Processing, MLSP, vol. 2019-October, IEEE Computer Society. https://doi.org/10.1109/MLSP.2019.8918874

Hilbert-Space Reduced-Rank Methods for Deep Gaussian Processes. / Emzir, Muhammad F.; Lasanen, Sari; Purisha, Zenith et al.
2019 IEEE 29th International Workshop on Machine Learning for Signal Processing, MLSP 2019. IEEE Computer Society, 2019. 8918874 (IEEE International Workshop on Machine Learning for Signal Processing, MLSP; Vol. 2019-October).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Hilbert-Space Reduced-Rank Methods for Deep Gaussian Processes

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AU - Lasanen, Sari

AU - Purisha, Zenith

AU - Sarkka, Simo

PY - 2019/10

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N2 - 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.

AB - 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.

KW - Bayesian inference

KW - Deep Gaussian processes

KW - Gaussian process

KW - Markov chain Monte Carlo

UR - https://www.scopus.com/pages/publications/85077703322

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DO - 10.1109/MLSP.2019.8918874

M3 - Conference contribution

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BT - 2019 IEEE 29th International Workshop on Machine Learning for Signal Processing, MLSP 2019

PB - IEEE Computer Society

ER -

Hilbert-Space Reduced-Rank Methods for Deep Gaussian Processes

Abstract

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Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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