Deconstructing cross-entropy for probabilistic binary classifiers

In this work, we analyze the cross-entropy function, widely used in classifiers both as a performance measure and as an optimization objective. We contextualize cross-entropy in the light of Bayesian decision theory, the formal probabilistic framework for making decisions, and we thoroughly analyze...

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Detalles Bibliográficos
Autores: Ramos Castro, Daniel, Franco-Pedroso, Javier, Lozano Díez, Alicia, González Rodríguez, Joaquín
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/683955
Acceso en línea:http://hdl.handle.net/10486/683955
https://dx.doi.org/10.3390/e20030208
Access Level:acceso abierto
Palabra clave:Bayesian
Calibration
Classifier
Cross-entropy
Discrimination
ECE plot
Probabilistic
Informática
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spelling Deconstructing cross-entropy for probabilistic binary classifiersRamos Castro, DanielFranco-Pedroso, JavierLozano Díez, AliciaGonzález Rodríguez, JoaquínBayesianCalibrationClassifierCross-entropyDiscriminationECE plotProbabilisticInformáticaIn this work, we analyze the cross-entropy function, widely used in classifiers both as a performance measure and as an optimization objective. We contextualize cross-entropy in the light of Bayesian decision theory, the formal probabilistic framework for making decisions, and we thoroughly analyze its motivation, meaning and interpretation from an information-theoretical point of view. In this sense, this article presents several contributions: First, we explicitly analyze the contribution to cross-entropy of (i) prior knowledge; and (ii) the value of the features in the form of a likelihood ratio. Second, we introduce a decomposition of cross-entropy into two components: discrimination and calibration. This decomposition enables the measurement of different performance aspects of a classifier in a more precise way; and justifies previously reported strategies to obtain reliable probabilities by means of the calibration of the output of a discriminating classifier. Third, we give different information-theoretical interpretations of cross-entropy, which can be useful in different application scenarios, and which are related to the concept of reference probabilities. Fourth, we present an analysis tool, the Empirical Cross-Entropy (ECE) plot, a compact representation of cross-entropy and its aforementioned decomposition. We show the power of ECE plots, as compared to other classical performance representations, in two diverse experimental examples: a speaker verification system, and a forensic case where some glass findings are present.MDPIDepartamento de Tecnología Electrónica y de las ComunicacionesEscuela Politécnica Superior20182018-03-01research articlehttp://purl.org/coar/resource_type/c_2df8fbb1VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10486/683955https://dx.doi.org/10.3390/e20030208reponame:Biblos-e Archivo. Repositorio Institucional de la UAMinstname:Universidad Autónoma de MadridInglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:repositorio.uam.es:10486/6839552026-06-23T12:46:27Z
dc.title.none.fl_str_mv Deconstructing cross-entropy for probabilistic binary classifiers
title Deconstructing cross-entropy for probabilistic binary classifiers
spellingShingle Deconstructing cross-entropy for probabilistic binary classifiers
Ramos Castro, Daniel
Bayesian
Calibration
Classifier
Cross-entropy
Discrimination
ECE plot
Probabilistic
Informática
title_short Deconstructing cross-entropy for probabilistic binary classifiers
title_full Deconstructing cross-entropy for probabilistic binary classifiers
title_fullStr Deconstructing cross-entropy for probabilistic binary classifiers
title_full_unstemmed Deconstructing cross-entropy for probabilistic binary classifiers
title_sort Deconstructing cross-entropy for probabilistic binary classifiers
dc.creator.none.fl_str_mv Ramos Castro, Daniel
Franco-Pedroso, Javier
Lozano Díez, Alicia
González Rodríguez, Joaquín
author Ramos Castro, Daniel
author_facet Ramos Castro, Daniel
Franco-Pedroso, Javier
Lozano Díez, Alicia
González Rodríguez, Joaquín
author_role author
author2 Franco-Pedroso, Javier
Lozano Díez, Alicia
González Rodríguez, Joaquín
author2_role author
author
author
dc.contributor.none.fl_str_mv Departamento de Tecnología Electrónica y de las Comunicaciones
Escuela Politécnica Superior
dc.subject.none.fl_str_mv Bayesian
Calibration
Classifier
Cross-entropy
Discrimination
ECE plot
Probabilistic
Informática
topic Bayesian
Calibration
Classifier
Cross-entropy
Discrimination
ECE plot
Probabilistic
Informática
description In this work, we analyze the cross-entropy function, widely used in classifiers both as a performance measure and as an optimization objective. We contextualize cross-entropy in the light of Bayesian decision theory, the formal probabilistic framework for making decisions, and we thoroughly analyze its motivation, meaning and interpretation from an information-theoretical point of view. In this sense, this article presents several contributions: First, we explicitly analyze the contribution to cross-entropy of (i) prior knowledge; and (ii) the value of the features in the form of a likelihood ratio. Second, we introduce a decomposition of cross-entropy into two components: discrimination and calibration. This decomposition enables the measurement of different performance aspects of a classifier in a more precise way; and justifies previously reported strategies to obtain reliable probabilities by means of the calibration of the output of a discriminating classifier. Third, we give different information-theoretical interpretations of cross-entropy, which can be useful in different application scenarios, and which are related to the concept of reference probabilities. Fourth, we present an analysis tool, the Empirical Cross-Entropy (ECE) plot, a compact representation of cross-entropy and its aforementioned decomposition. We show the power of ECE plots, as compared to other classical performance representations, in two diverse experimental examples: a speaker verification system, and a forensic case where some glass findings are present.
publishDate 2018
dc.date.none.fl_str_mv 2018
2018-03-01
dc.type.none.fl_str_mv research article
http://purl.org/coar/resource_type/c_2df8fbb1
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10486/683955
https://dx.doi.org/10.3390/e20030208
url http://hdl.handle.net/10486/683955
https://dx.doi.org/10.3390/e20030208
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv MDPI
publisher.none.fl_str_mv MDPI
dc.source.none.fl_str_mv reponame:Biblos-e Archivo. Repositorio Institucional de la UAM
instname:Universidad Autónoma de Madrid
instname_str Universidad Autónoma de Madrid
reponame_str Biblos-e Archivo. Repositorio Institucional de la UAM
collection Biblos-e Archivo. Repositorio Institucional de la UAM
repository.name.fl_str_mv
repository.mail.fl_str_mv
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