Asymptotics of Maximum Likelihood Parameter Estimates for Gaussian Processes: The Ornstein-Uhlenbeck Prior

Toni Karvonen; Filip Tronarp; Simo Särkkä

doi:10.1109/MLSP.2019.8918767

Asymptotics of Maximum Likelihood Parameter Estimates for Gaussian Processes: The Ornstein-Uhlenbeck Prior

Toni Karvonen, Filip Tronarp, Simo Särkkä

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

3 Sitaatiot (Scopus)

Abstrakti

This article studies the maximum likelihood estimates of magnitude and scale parameters for a Gaussian process of Ornstein-Uhlenbeck type used to model a deterministic function that does not have to be a realisation of an Ornstein- Uhlenbeck process. Specifically, we derive explicit expressions for the limiting values of the maximum likelihood estimates as the number of observations increases. The results demonstrate that the function typically needs to be sufficiently similar to a sample path of an Ornstein-Uhlenbeck process or have discontinuities if the variance of the model is to remain non-zero. Numerical examples illustrate the behaviour of the estimates when the function is not a sample path of any Ornstein-Uhlenbeck process.

Alkuperäiskieli	Englanti
Otsikko	Proceedings of the 29th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2019
Kustantaja	IEEE
Sivumäärä	6
ISBN (elektroninen)	9781728108247
DOI - pysyväislinkit	https://doi.org/10.1109/MLSP.2019.8918767
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

Pääsy asiakirjaan

10.1109/MLSP.2019.8918767

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Link to publication in Scopus

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Karvonen, T., Tronarp, F., & Särkkä, S. (2019). Asymptotics of Maximum Likelihood Parameter Estimates for Gaussian Processes: The Ornstein-Uhlenbeck Prior. teoksessa Proceedings of the 29th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2019 Artikkeli 8918767 (IEEE International Workshop on Machine Learning for Signal Processing). IEEE. https://doi.org/10.1109/MLSP.2019.8918767

@inproceedings{4fdd1170d9674991be9ba2254b98ca3a,

title = "Asymptotics of Maximum Likelihood Parameter Estimates for Gaussian Processes: The Ornstein-Uhlenbeck Prior",

abstract = "This article studies the maximum likelihood estimates of magnitude and scale parameters for a Gaussian process of Ornstein-Uhlenbeck type used to model a deterministic function that does not have to be a realisation of an Ornstein- Uhlenbeck process. Specifically, we derive explicit expressions for the limiting values of the maximum likelihood estimates as the number of observations increases. The results demonstrate that the function typically needs to be sufficiently similar to a sample path of an Ornstein-Uhlenbeck process or have discontinuities if the variance of the model is to remain non-zero. Numerical examples illustrate the behaviour of the estimates when the function is not a sample path of any Ornstein-Uhlenbeck process.",

keywords = "Gaussian process regression, Maximum likelihood estimation, Ornstein- Uhlenbeck process, Probabilistic numerics",

author = "Toni Karvonen and Filip Tronarp and Simo S{\"a}rkk{\"a}",

year = "2019",

month = oct,

day = "1",

doi = "10.1109/MLSP.2019.8918767",

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",

}

Karvonen, T, Tronarp, F & Särkkä, S 2019, Asymptotics of Maximum Likelihood Parameter Estimates for Gaussian Processes: The Ornstein-Uhlenbeck Prior. julkaisussa Proceedings of the 29th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2019., 8918767, 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.2019.8918767

Asymptotics of Maximum Likelihood Parameter Estimates for Gaussian Processes: The Ornstein-Uhlenbeck Prior. / Karvonen, Toni; Tronarp, Filip; Särkkä, Simo.
Proceedings of the 29th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2019. IEEE, 2019. 8918767 (IEEE International Workshop on Machine Learning for Signal Processing).

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

TY - GEN

T1 - Asymptotics of Maximum Likelihood Parameter Estimates for Gaussian Processes

T2 - IEEE International Workshop on Machine Learning for Signal Processing

AU - Karvonen, Toni

AU - Tronarp, Filip

AU - Särkkä, Simo

N1 - Conference code: 29

PY - 2019/10/1

Y1 - 2019/10/1

N2 - This article studies the maximum likelihood estimates of magnitude and scale parameters for a Gaussian process of Ornstein-Uhlenbeck type used to model a deterministic function that does not have to be a realisation of an Ornstein- Uhlenbeck process. Specifically, we derive explicit expressions for the limiting values of the maximum likelihood estimates as the number of observations increases. The results demonstrate that the function typically needs to be sufficiently similar to a sample path of an Ornstein-Uhlenbeck process or have discontinuities if the variance of the model is to remain non-zero. Numerical examples illustrate the behaviour of the estimates when the function is not a sample path of any Ornstein-Uhlenbeck process.

AB - This article studies the maximum likelihood estimates of magnitude and scale parameters for a Gaussian process of Ornstein-Uhlenbeck type used to model a deterministic function that does not have to be a realisation of an Ornstein- Uhlenbeck process. Specifically, we derive explicit expressions for the limiting values of the maximum likelihood estimates as the number of observations increases. The results demonstrate that the function typically needs to be sufficiently similar to a sample path of an Ornstein-Uhlenbeck process or have discontinuities if the variance of the model is to remain non-zero. Numerical examples illustrate the behaviour of the estimates when the function is not a sample path of any Ornstein-Uhlenbeck process.

KW - Gaussian process regression

KW - Maximum likelihood estimation

KW - Ornstein- Uhlenbeck process

KW - Probabilistic numerics

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U2 - 10.1109/MLSP.2019.8918767

DO - 10.1109/MLSP.2019.8918767

M3 - Conference article in proceedings

AN - SCOPUS:85077712808

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

Y2 - 13 October 2019 through 16 October 2019

ER -

Karvonen T, Tronarp F, Särkkä S. Asymptotics of Maximum Likelihood Parameter Estimates for Gaussian Processes: The Ornstein-Uhlenbeck Prior. julkaisussa Proceedings of the 29th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2019. IEEE. 2019. 8918767. (IEEE International Workshop on Machine Learning for Signal Processing). doi: 10.1109/MLSP.2019.8918767

Asymptotics of Maximum Likelihood Parameter Estimates for Gaussian Processes: The Ornstein-Uhlenbeck Prior

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