Generalizing the Balance Heuristic Estimator in Multiple Importance Sampling

In this paper, we propose a novel and generic family of multiple importance sampling estimators. We first revisit the celebrated balance heuristic estimator, a widely used Monte Carlo technique for the approximation of intractable integrals. Then, we establish a generalized framework for the combina...

Descripción completa

Detalles Bibliográficos
Autores: Sbert, Mateu, Elvira, Víctor
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2022
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:10256/20669
Acceso en línea:http://hdl.handle.net/10256/20669
Access Level:acceso abierto
Palabra clave:Montecarlo, Mètode de
Monte Carlo method
Estimació, Teoria de l'
Estimation, Théorie de l'
Entropia creuada, Mètode d'
Cross-entropy method
id ES_20cc808f790ec9e18c08c97087fd3abc
oai_identifier_str oai:recercat.cat:10256/20669
network_acronym_str ES
network_name_str España
repository_id_str
spelling Generalizing the Balance Heuristic Estimator in Multiple Importance SamplingSbert, MateuElvira, VíctorMontecarlo, Mètode deMonte Carlo methodEstimació, Teoria de l'Estimation, Théorie de l'Entropia creuada, Mètode d'Cross-entropy methodIn this paper, we propose a novel and generic family of multiple importance sampling estimators. We first revisit the celebrated balance heuristic estimator, a widely used Monte Carlo technique for the approximation of intractable integrals. Then, we establish a generalized framework for the combination of samples simulated from multiple proposals. Our approach is based on considering as free parameters both the sampling rates and the combination coefficients, which are the same in the balance heuristics estimator. Thus our novel framework contains the balance heuristic as a particular case. We study the optimal choice of the free parameters in such a way that the variance of the resulting estimator is minimized. A theoretical variance study shows the optimal solution is always better than the balance heuristic estimator (except in degenerate cases where both are the same). We also give sufficient conditions on the parameter values for the new generalized estimator to be better than the balance heuristic estimator, and one necessary and sufficient condition related to χ2 divergence. Using five numerical examples, we first show the gap in the efficiency of both new and classical balance heuristic estimators, for equal sampling and for several state of the art sampling rates. Then, for these five examples, we find the variances for some notable selection of parameters showing that, for the important case of equal count of samples, our new estimator with an optimal selection of parameters outperforms the classical balance heuristic. Finally, new heuristics are introduced that exploit the theoretical findingsMDPI (Multidisciplinary Digital Publishing Institute)2022info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionpeer-reviewedapplication/pdfhttp://hdl.handle.net/10256/20669http://hdl.handle.net/10256/20669Entropy, 2022, vol. 24, núm. 2, p. 191Articles publicats (D-IMA)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)Inglésinfo:eu-repo/semantics/altIdentifier/doi/10.3390/e24020191info:eu-repo/semantics/altIdentifier/eissn/1099-4300Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:recercat.cat:10256/206692026-05-29T05:05:01Z
dc.title.none.fl_str_mv Generalizing the Balance Heuristic Estimator in Multiple Importance Sampling
title Generalizing the Balance Heuristic Estimator in Multiple Importance Sampling
spellingShingle Generalizing the Balance Heuristic Estimator in Multiple Importance Sampling
Sbert, Mateu
Montecarlo, Mètode de
Monte Carlo method
Estimació, Teoria de l'
Estimation, Théorie de l'
Entropia creuada, Mètode d'
Cross-entropy method
title_short Generalizing the Balance Heuristic Estimator in Multiple Importance Sampling
title_full Generalizing the Balance Heuristic Estimator in Multiple Importance Sampling
title_fullStr Generalizing the Balance Heuristic Estimator in Multiple Importance Sampling
title_full_unstemmed Generalizing the Balance Heuristic Estimator in Multiple Importance Sampling
title_sort Generalizing the Balance Heuristic Estimator in Multiple Importance Sampling
dc.creator.none.fl_str_mv Sbert, Mateu
Elvira, Víctor
author Sbert, Mateu
author_facet Sbert, Mateu
Elvira, Víctor
author_role author
author2 Elvira, Víctor
author2_role author
dc.subject.none.fl_str_mv Montecarlo, Mètode de
Monte Carlo method
Estimació, Teoria de l'
Estimation, Théorie de l'
Entropia creuada, Mètode d'
Cross-entropy method
topic Montecarlo, Mètode de
Monte Carlo method
Estimació, Teoria de l'
Estimation, Théorie de l'
Entropia creuada, Mètode d'
Cross-entropy method
description In this paper, we propose a novel and generic family of multiple importance sampling estimators. We first revisit the celebrated balance heuristic estimator, a widely used Monte Carlo technique for the approximation of intractable integrals. Then, we establish a generalized framework for the combination of samples simulated from multiple proposals. Our approach is based on considering as free parameters both the sampling rates and the combination coefficients, which are the same in the balance heuristics estimator. Thus our novel framework contains the balance heuristic as a particular case. We study the optimal choice of the free parameters in such a way that the variance of the resulting estimator is minimized. A theoretical variance study shows the optimal solution is always better than the balance heuristic estimator (except in degenerate cases where both are the same). We also give sufficient conditions on the parameter values for the new generalized estimator to be better than the balance heuristic estimator, and one necessary and sufficient condition related to χ2 divergence. Using five numerical examples, we first show the gap in the efficiency of both new and classical balance heuristic estimators, for equal sampling and for several state of the art sampling rates. Then, for these five examples, we find the variances for some notable selection of parameters showing that, for the important case of equal count of samples, our new estimator with an optimal selection of parameters outperforms the classical balance heuristic. Finally, new heuristics are introduced that exploit the theoretical findings
publishDate 2022
dc.date.none.fl_str_mv 2022
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
peer-reviewed
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10256/20669
http://hdl.handle.net/10256/20669
url http://hdl.handle.net/10256/20669
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.3390/e24020191
info:eu-repo/semantics/altIdentifier/eissn/1099-4300
dc.rights.none.fl_str_mv Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv MDPI (Multidisciplinary Digital Publishing Institute)
publisher.none.fl_str_mv MDPI (Multidisciplinary Digital Publishing Institute)
dc.source.none.fl_str_mv Entropy, 2022, vol. 24, núm. 2, p. 191
Articles publicats (D-IMA)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869404479886983168
score 15,811543

Similares en LA Referencia