A Novel Nonparametric Distance Estimator for Densities with Error Bounds
Autor(a) principal: | |
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Data de Publicação: | 2013 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | https://repositorio-aberto.up.pt/handle/10216/66052 |
Resumo: | The use of a metric to assess distance between probability densities is an important practical problem. In this work, a particular metric induced by an a-divergence is studied. The Hellinger metric can be interpreted as a particular case within the framework of generalized Tsallis divergences and entropies. The nonparametric Parzen's density estimator emerges as a natural candidate to estimate the underlying probability density function, since it may account for data from different groups, or experiments with distinct instrumental precisions, i.e., non-independent and identically distributed (non-i.i.d.) data. However, the information theoretic derived metric of the nonparametric Parzen's density estimator displays infinite variance, limiting the direct use of resampling estimators. Based on measure theory, we present a change of measure to build a finite variance density allowing the use of resampling estimators. In order to counteract the poor scaling with dimension, we propose a new nonparametric two-stage robust resampling estimator of Hellinger's metric error bounds for heterocedastic data. The approach presents very promising results allowing the use of different covariances for different clusters with impact on the distance evaluation. |
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A Novel Nonparametric Distance Estimator for Densities with Error BoundsCiências Tecnológicas, Ciências da engenharia e tecnologiasTechnological sciences, Engineering and technologyThe use of a metric to assess distance between probability densities is an important practical problem. In this work, a particular metric induced by an a-divergence is studied. The Hellinger metric can be interpreted as a particular case within the framework of generalized Tsallis divergences and entropies. The nonparametric Parzen's density estimator emerges as a natural candidate to estimate the underlying probability density function, since it may account for data from different groups, or experiments with distinct instrumental precisions, i.e., non-independent and identically distributed (non-i.i.d.) data. However, the information theoretic derived metric of the nonparametric Parzen's density estimator displays infinite variance, limiting the direct use of resampling estimators. Based on measure theory, we present a change of measure to build a finite variance density allowing the use of resampling estimators. In order to counteract the poor scaling with dimension, we propose a new nonparametric two-stage robust resampling estimator of Hellinger's metric error bounds for heterocedastic data. The approach presents very promising results allowing the use of different covariances for different clusters with impact on the distance evaluation.20132013-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://repositorio-aberto.up.pt/handle/10216/66052eng1099-430010.3390/e15051609Alexandre R. F. CarvalhoJoão Manuel R. S. TavaresJosé C. Principeinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-11-29T14:59:29Zoai:repositorio-aberto.up.pt:10216/66052Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T00:13:08.583645Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
A Novel Nonparametric Distance Estimator for Densities with Error Bounds |
title |
A Novel Nonparametric Distance Estimator for Densities with Error Bounds |
spellingShingle |
A Novel Nonparametric Distance Estimator for Densities with Error Bounds Alexandre R. F. Carvalho Ciências Tecnológicas, Ciências da engenharia e tecnologias Technological sciences, Engineering and technology |
title_short |
A Novel Nonparametric Distance Estimator for Densities with Error Bounds |
title_full |
A Novel Nonparametric Distance Estimator for Densities with Error Bounds |
title_fullStr |
A Novel Nonparametric Distance Estimator for Densities with Error Bounds |
title_full_unstemmed |
A Novel Nonparametric Distance Estimator for Densities with Error Bounds |
title_sort |
A Novel Nonparametric Distance Estimator for Densities with Error Bounds |
author |
Alexandre R. F. Carvalho |
author_facet |
Alexandre R. F. Carvalho João Manuel R. S. Tavares José C. Principe |
author_role |
author |
author2 |
João Manuel R. S. Tavares José C. Principe |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Alexandre R. F. Carvalho João Manuel R. S. Tavares José C. Principe |
dc.subject.por.fl_str_mv |
Ciências Tecnológicas, Ciências da engenharia e tecnologias Technological sciences, Engineering and technology |
topic |
Ciências Tecnológicas, Ciências da engenharia e tecnologias Technological sciences, Engineering and technology |
description |
The use of a metric to assess distance between probability densities is an important practical problem. In this work, a particular metric induced by an a-divergence is studied. The Hellinger metric can be interpreted as a particular case within the framework of generalized Tsallis divergences and entropies. The nonparametric Parzen's density estimator emerges as a natural candidate to estimate the underlying probability density function, since it may account for data from different groups, or experiments with distinct instrumental precisions, i.e., non-independent and identically distributed (non-i.i.d.) data. However, the information theoretic derived metric of the nonparametric Parzen's density estimator displays infinite variance, limiting the direct use of resampling estimators. Based on measure theory, we present a change of measure to build a finite variance density allowing the use of resampling estimators. In order to counteract the poor scaling with dimension, we propose a new nonparametric two-stage robust resampling estimator of Hellinger's metric error bounds for heterocedastic data. The approach presents very promising results allowing the use of different covariances for different clusters with impact on the distance evaluation. |
publishDate |
2013 |
dc.date.none.fl_str_mv |
2013 2013-01-01T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://repositorio-aberto.up.pt/handle/10216/66052 |
url |
https://repositorio-aberto.up.pt/handle/10216/66052 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1099-4300 10.3390/e15051609 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799136053583413248 |