A Double Proposal Normalized Importance Sampling Estimator

Roland Lamberti; Yohan Petetin; Francois Septier; Francois Desbouvries

doi:10.1109/SSP.2018.8450849

A Double Proposal Normalized Importance Sampling Estimator

Roland Lamberti, Yohan Petetin, Francois Septier, Francois Desbouvries

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

Abstract

Monte Carlo methods are widely used in signal processing for computing integrals of interest. Among Monte Carlo methods, Importance Sampling is a variance reduction technique which consists in sampling from an instrumental distribution and reweighting the samples in order to correct the discrepancy between the target and proposal distributions. When either the target or the proposal distribution is known only up to a constant, the moment of interest can be rewritten as a ratio of two expectations, which can be approximated via self-normalized importance sampling. In this paper we show that it is possible to improve the self-normalized importance sampling estimate by approximating the two expectations in this ratio via two importance distributions. In order to tune them we optimize the variance of the final estimate under a reasonable constraint. Our results are validated via simulations.

Original language	English
Title of host publication	2018 IEEE Statistical Signal Processing Workshop, SSP 2018
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	253-257
Number of pages	5
ISBN (Print)	9781538615706
DOIs	https://doi.org/10.1109/SSP.2018.8450849
Publication status	Published - 29 Aug 2018
Externally published	Yes
Event	20th IEEE Statistical Signal Processing Workshop, SSP 2018 - Freiburg im Breisgau, Germany Duration: 10 Jun 2018 → 13 Jun 2018

Publication series

Name	2018 IEEE Statistical Signal Processing Workshop, SSP 2018

Conference

Conference	20th IEEE Statistical Signal Processing Workshop, SSP 2018
Country/Territory	Germany
City	Freiburg im Breisgau
Period	10/06/18 → 13/06/18

Keywords

(self-normalized) importance sampling
Monte Carlo integration
variance minimization

Access to Document

10.1109/SSP.2018.8450849

Cite this

Lamberti, R., Petetin, Y., Septier, F., & Desbouvries, F. (2018). A Double Proposal Normalized Importance Sampling Estimator. In 2018 IEEE Statistical Signal Processing Workshop, SSP 2018 (pp. 253-257). Article 8450849 (2018 IEEE Statistical Signal Processing Workshop, SSP 2018). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/SSP.2018.8450849

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title = "A Double Proposal Normalized Importance Sampling Estimator",

abstract = "Monte Carlo methods are widely used in signal processing for computing integrals of interest. Among Monte Carlo methods, Importance Sampling is a variance reduction technique which consists in sampling from an instrumental distribution and reweighting the samples in order to correct the discrepancy between the target and proposal distributions. When either the target or the proposal distribution is known only up to a constant, the moment of interest can be rewritten as a ratio of two expectations, which can be approximated via self-normalized importance sampling. In this paper we show that it is possible to improve the self-normalized importance sampling estimate by approximating the two expectations in this ratio via two importance distributions. In order to tune them we optimize the variance of the final estimate under a reasonable constraint. Our results are validated via simulations.",

keywords = "(self-normalized) importance sampling, Monte Carlo integration, variance minimization",

author = "Roland Lamberti and Yohan Petetin and Francois Septier and Francois Desbouvries",

note = "Publisher Copyright: {\textcopyright} 2018 IEEE.; 20th IEEE Statistical Signal Processing Workshop, SSP 2018 ; Conference date: 10-06-2018 Through 13-06-2018",

year = "2018",

month = aug,

day = "29",

doi = "10.1109/SSP.2018.8450849",

language = "English",

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Lamberti, R, Petetin, Y, Septier, F & Desbouvries, F 2018, A Double Proposal Normalized Importance Sampling Estimator. in 2018 IEEE Statistical Signal Processing Workshop, SSP 2018., 8450849, 2018 IEEE Statistical Signal Processing Workshop, SSP 2018, Institute of Electrical and Electronics Engineers Inc., pp. 253-257, 20th IEEE Statistical Signal Processing Workshop, SSP 2018, Freiburg im Breisgau, Germany, 10/06/18. https://doi.org/10.1109/SSP.2018.8450849

A Double Proposal Normalized Importance Sampling Estimator. / Lamberti, Roland; Petetin, Yohan; Septier, Francois et al.
2018 IEEE Statistical Signal Processing Workshop, SSP 2018. Institute of Electrical and Electronics Engineers Inc., 2018. p. 253-257 8450849 (2018 IEEE Statistical Signal Processing Workshop, SSP 2018).

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

TY - GEN

T1 - A Double Proposal Normalized Importance Sampling Estimator

AU - Lamberti, Roland

AU - Petetin, Yohan

AU - Septier, Francois

AU - Desbouvries, Francois

PY - 2018/8/29

Y1 - 2018/8/29

N2 - Monte Carlo methods are widely used in signal processing for computing integrals of interest. Among Monte Carlo methods, Importance Sampling is a variance reduction technique which consists in sampling from an instrumental distribution and reweighting the samples in order to correct the discrepancy between the target and proposal distributions. When either the target or the proposal distribution is known only up to a constant, the moment of interest can be rewritten as a ratio of two expectations, which can be approximated via self-normalized importance sampling. In this paper we show that it is possible to improve the self-normalized importance sampling estimate by approximating the two expectations in this ratio via two importance distributions. In order to tune them we optimize the variance of the final estimate under a reasonable constraint. Our results are validated via simulations.

AB - Monte Carlo methods are widely used in signal processing for computing integrals of interest. Among Monte Carlo methods, Importance Sampling is a variance reduction technique which consists in sampling from an instrumental distribution and reweighting the samples in order to correct the discrepancy between the target and proposal distributions. When either the target or the proposal distribution is known only up to a constant, the moment of interest can be rewritten as a ratio of two expectations, which can be approximated via self-normalized importance sampling. In this paper we show that it is possible to improve the self-normalized importance sampling estimate by approximating the two expectations in this ratio via two importance distributions. In order to tune them we optimize the variance of the final estimate under a reasonable constraint. Our results are validated via simulations.

KW - (self-normalized) importance sampling

KW - Monte Carlo integration

KW - variance minimization

U2 - 10.1109/SSP.2018.8450849

DO - 10.1109/SSP.2018.8450849

M3 - Conference contribution

AN - SCOPUS:85053843756

SN - 9781538615706

T3 - 2018 IEEE Statistical Signal Processing Workshop, SSP 2018

SP - 253

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BT - 2018 IEEE Statistical Signal Processing Workshop, SSP 2018

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 20th IEEE Statistical Signal Processing Workshop, SSP 2018

Y2 - 10 June 2018 through 13 June 2018

ER -

A Double Proposal Normalized Importance Sampling Estimator

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Keywords

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