Hilbert-Space Reduced-Rank Methods for Deep Gaussian Processes

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

doi:10.1109/MLSP.2019.8918874

Hilbert-Space Reduced-Rank Methods for Deep Gaussian Processes

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

Lappeenranta University of Technology

Tutkimustuotos: Artikkeli kirjassa/konferenssijulkaisussa › Conference article in proceedings › Scientific › vertaisarvioitu

6 Sitaatiot (Scopus)

Abstrakti

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.

Alkuperäiskieli	Englanti
Otsikko	Proceedings of the 29th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2019
Kustantaja	IEEE
ISBN (elektroninen)	9781728108247
DOI - pysyväislinkit	https://doi.org/10.1109/MLSP.2019.8918874
Tila	Julkaistu - 1 lokak. 2019
OKM-julkaisutyyppi	A4 Artikkeli konferenssijulkaisussa
Tapahtuma	IEEE International Workshop on Machine Learning for Signal Processing - Pittsburgh, Yhdysvallat Kesto: 13 lokak. 2019 → 16 lokak. 2019 Konferenssinumero: 29

Julkaisusarja

Nimi	IEEE International Workshop on Machine Learning for Signal Processing
Kustantaja	IEEE
ISSN (painettu)	2161-0363
ISSN (elektroninen)	2161-0371

Workshop

Workshop	IEEE International Workshop on Machine Learning for Signal Processing
Lyhennettä	MLSP
Maa/Alue	Yhdysvallat
Kaupunki	Pittsburgh
Ajanjakso	13/10/2019 → 16/10/2019

Rahoitus

∗This work is supported by the Academy Finland grant numbers 313708 and 314474.

Pääsy asiakirjaan

10.1109/MLSP.2019.8918874

Muut tiedostot ja linkit

Link to publication in Scopus

2 Päättynyt

Probabilistinen syväoppiminen hierarkkisilla stokastisilla osittaisdifferentiaaliyhtälöillä
Särkkä, S. (Vastuullinen johtaja), Gao, R. (Projektin jäsen), Hostettler, R. (Projektin jäsen), Karvonen, T. (Projektin jäsen), Sarmavuori, J. (Projektin jäsen), Purisha, Z. (Projektin jäsen), Bahrami Rad, A. (Projektin jäsen), Raitoharju, M. (Projektin jäsen), Emzir, M. (Projektin jäsen) & Tronarp, F. (Projektin jäsen)
01/01/2018 → 31/12/2019
Projekti: Academy of Finland: Other research funding
Monispektrinen fotonilaskenta lääketieteelliseen kuvantamiseen sekä hiukkassuihkun ominaisuuksien määrittämiseen
Särkkä, S. (Vastuullinen johtaja), Purisha, Z. (Projektin jäsen), Gao, R. (Projektin jäsen), Tronarp, F. (Projektin jäsen), Yamin, A. (Projektin jäsen), Hassan, S. S. (Projektin jäsen), Zhao, Z. (Projektin jäsen), Emzir, M. (Projektin jäsen) & Sarmavuori, J. (Projektin jäsen)
01/01/2018 → 31/12/2021
Projekti: Academy of Finland: Other research funding

Siteeraa tätä

Emzir, M. F., Lasanen, S., Purisha, Z., & Särkkä, S. (2019). Hilbert-Space Reduced-Rank Methods for Deep Gaussian Processes. teoksessa Proceedings of the 29th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2019 Artikkeli 8918874 (IEEE International Workshop on Machine Learning for Signal Processing). IEEE. https://doi.org/10.1109/MLSP.2019.8918874

@inproceedings{8b94835eeccb4d91b475e539bfc71473,

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 S{\"a}rkk{\"a}",

year = "2019",

month = oct,

day = "1",

doi = "10.1109/MLSP.2019.8918874",

language = "English",

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

publisher = "IEEE",

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

address = "United States",

note = "IEEE International Workshop on Machine Learning for Signal Processing, MLSP ; Conference date: 13-10-2019 Through 16-10-2019",

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Emzir, MF, Lasanen, S, Purisha, Z & Särkkä, S 2019, Hilbert-Space Reduced-Rank Methods for Deep Gaussian Processes. julkaisussa Proceedings of the 29th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2019., 8918874, IEEE International Workshop on Machine Learning for Signal Processing, IEEE, IEEE International Workshop on Machine Learning for Signal Processing, Pittsburgh, Pennsylvania, Yhdysvallat, 13/10/2019. 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.
Proceedings of the 29th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2019. IEEE, 2019. 8918874 (IEEE International Workshop on Machine Learning for Signal Processing).

Tutkimustuotos: Artikkeli kirjassa/konferenssijulkaisussa › Conference article in proceedings › Scientific › vertaisarvioitu

TY - GEN

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

AU - Emzir, Muhammad F.

AU - Lasanen, Sari

AU - Purisha, Zenith

AU - Särkkä, Simo

N1 - Conference code: 29

PY - 2019/10/1

Y1 - 2019/10/1

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

U2 - 10.1109/MLSP.2019.8918874

DO - 10.1109/MLSP.2019.8918874

M3 - Conference article in proceedings

AN - SCOPUS:85077703322

T3 - IEEE International Workshop on Machine Learning for Signal Processing

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

PB - IEEE

T2 - IEEE International Workshop on Machine Learning for Signal Processing

Y2 - 13 October 2019 through 16 October 2019

ER -

Hilbert-Space Reduced-Rank Methods for Deep Gaussian Processes

Abstrakti

Julkaisusarja

Workshop

Rahoitus

Pääsy asiakirjaan

Muut tiedostot ja linkit

Sormenjälki

Projektit

Probabilistinen syväoppiminen hierarkkisilla stokastisilla osittaisdifferentiaaliyhtälöillä

Monispektrinen fotonilaskenta lääketieteelliseen kuvantamiseen sekä hiukkassuihkun ominaisuuksien määrittämiseen

Siteeraa tätä