Gaussian Approximations of SDES in Metropolis-Adjusted Langevin Algorithms

Simo Särkkä; Christos Merkatas; Toni Karvonen

doi:10.1109/MLSP52302.2021.9596301

Gaussian Approximations of SDES in Metropolis-Adjusted Langevin Algorithms

Simo Särkkä, Christos Merkatas, Toni Karvonen

Alan Turing Institute

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

171 Downloads (Pure)

Abstract

Markov chain Monte Carlo (MCMC) methods are a cornerstone of Bayesian inference and stochastic simulation. The Metropolis-adjusted Langevin algorithm (MALA) is an MCMC method that relies on the simulation of a stochastic differential equation (SDE) whose stationary distribution is the desired target density using the Euler-Maruyama algorithm and accounts for simulation errors using a Metropolis step. In this paper we propose a modification of the MALA which uses Gaussian assumed density approximations for the integration of the SDE. The effectiveness of the algorithm is illustrated on simulated and real data sets.

Original language	English
Title of host publication	2021 IEEE 31st International Workshop on Machine Learning for Signal Processing, MLSP 2021
Publisher	IEEE
Pages	1-6
Number of pages	6
ISBN (Electronic)	978-1-7281-6338-3
ISBN (Print)	978-1-6654-1184-4
DOIs	https://doi.org/10.1109/MLSP52302.2021.9596301
Publication status	Published - 15 Nov 2021
MoE publication type	A4 Conference publication
Event	IEEE International Workshop on Machine Learning for Signal Processing - Gold Coast, Australia Duration: 25 Oct 2021 → 28 Oct 2021 Conference number: 31 https://2021.ieeemlsp.org/

Publication series

Name	Machine learning for signal processing
ISSN (Print)	1551-2541

Workshop

Workshop	IEEE International Workshop on Machine Learning for Signal Processing
Abbreviated title	MLSP
Country/Territory	Australia
City	Gold Coast
Period	25/10/2021 → 28/10/2021
Internet address	https://2021.ieeemlsp.org/

Keywords

Monte Carlo methods
Machine learning algorithms
Heuristic algorithms
Signal processing algorithms
Machine learning
Signal processing
Markov processes

Access to Document

10.1109/MLSP52302.2021.9596301

ELEC_Särkkä_etal_Gaussian_approximations_of_SDEs_MLSP2021Accepted author manuscript, 450 KB

Cite this

@inproceedings{7191685f7c4e4b6ab0abff5c8d59efbb,

title = "Gaussian Approximations of SDES in Metropolis-Adjusted Langevin Algorithms",

abstract = "Markov chain Monte Carlo (MCMC) methods are a cornerstone of Bayesian inference and stochastic simulation. The Metropolis-adjusted Langevin algorithm (MALA) is an MCMC method that relies on the simulation of a stochastic differential equation (SDE) whose stationary distribution is the desired target density using the Euler-Maruyama algorithm and accounts for simulation errors using a Metropolis step. In this paper we propose a modification of the MALA which uses Gaussian assumed density approximations for the integration of the SDE. The effectiveness of the algorithm is illustrated on simulated and real data sets.",

keywords = "Monte Carlo methods, Machine learning algorithms, Heuristic algorithms, Signal processing algorithms, Machine learning, Signal processing, Markov processes",

author = "Simo S{\"a}rkk{\"a} and Christos Merkatas and Toni Karvonen",

year = "2021",

month = nov,

day = "15",

doi = "10.1109/MLSP52302.2021.9596301",

language = "English",

isbn = "978-1-6654-1184-4",

series = "Machine learning for signal processing",

publisher = "IEEE",

pages = "1--6",

booktitle = "2021 IEEE 31st International Workshop on Machine Learning for Signal Processing, MLSP 2021",

address = "United States",

note = "IEEE International Workshop on Machine Learning for Signal Processing , MLSP ; Conference date: 25-10-2021 Through 28-10-2021",

url = "https://2021.ieeemlsp.org/",

}

Särkkä, S, Merkatas, C & Karvonen, T 2021, Gaussian Approximations of SDES in Metropolis-Adjusted Langevin Algorithms. in 2021 IEEE 31st International Workshop on Machine Learning for Signal Processing, MLSP 2021., 9596301, Machine learning for signal processing, IEEE, pp. 1-6, IEEE International Workshop on Machine Learning for Signal Processing , Gold Coast, Australia, 25/10/2021. https://doi.org/10.1109/MLSP52302.2021.9596301

Gaussian Approximations of SDES in Metropolis-Adjusted Langevin Algorithms. / Särkkä, Simo; Merkatas, Christos; Karvonen, Toni.
2021 IEEE 31st International Workshop on Machine Learning for Signal Processing, MLSP 2021. IEEE, 2021. p. 1-6 9596301 (Machine learning for signal processing).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

TY - GEN

T1 - Gaussian Approximations of SDES in Metropolis-Adjusted Langevin Algorithms

AU - Särkkä, Simo

AU - Merkatas, Christos

AU - Karvonen, Toni

N1 - Conference code: 31

PY - 2021/11/15

Y1 - 2021/11/15

N2 - Markov chain Monte Carlo (MCMC) methods are a cornerstone of Bayesian inference and stochastic simulation. The Metropolis-adjusted Langevin algorithm (MALA) is an MCMC method that relies on the simulation of a stochastic differential equation (SDE) whose stationary distribution is the desired target density using the Euler-Maruyama algorithm and accounts for simulation errors using a Metropolis step. In this paper we propose a modification of the MALA which uses Gaussian assumed density approximations for the integration of the SDE. The effectiveness of the algorithm is illustrated on simulated and real data sets.

AB - Markov chain Monte Carlo (MCMC) methods are a cornerstone of Bayesian inference and stochastic simulation. The Metropolis-adjusted Langevin algorithm (MALA) is an MCMC method that relies on the simulation of a stochastic differential equation (SDE) whose stationary distribution is the desired target density using the Euler-Maruyama algorithm and accounts for simulation errors using a Metropolis step. In this paper we propose a modification of the MALA which uses Gaussian assumed density approximations for the integration of the SDE. The effectiveness of the algorithm is illustrated on simulated and real data sets.

KW - Monte Carlo methods

KW - Machine learning algorithms

KW - Heuristic algorithms

KW - Signal processing algorithms

KW - Machine learning

KW - Signal processing

KW - Markov processes

UR - http://www.scopus.com/inward/record.url?scp=85122809655&partnerID=8YFLogxK

U2 - 10.1109/MLSP52302.2021.9596301

DO - 10.1109/MLSP52302.2021.9596301

M3 - Conference article in proceedings

SN - 978-1-6654-1184-4

T3 - Machine learning for signal processing

SP - 1

EP - 6

BT - 2021 IEEE 31st International Workshop on Machine Learning for Signal Processing, MLSP 2021

PB - IEEE

T2 - IEEE International Workshop on Machine Learning for Signal Processing

Y2 - 25 October 2021 through 28 October 2021

ER -

Gaussian Approximations of SDES in Metropolis-Adjusted Langevin Algorithms

Abstract

Publication series

Workshop

Keywords

Access to Document

Other files and links

Fingerprint

ADAFUME: Advanced data fusion methods for environmental modeling

Science-IT

Cite this

Gaussian Approximations of SDES in Metropolis-Adjusted Langevin Algorithms

Abstract

Publication series

Workshop

Keywords

Access to Document

Other files and links

Fingerprint

Projects

ADAFUME: Advanced data fusion methods for environmental modeling

Equipment

Science-IT

Cite this