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On optimal Bayesian classification and risk estimation under multiple classes
A recently proposed optimal Bayesian classification paradigm addresses optimal error rate analysis for small-sample discrimination, including optimal classifiers, optimal error estimators, and error estimation analysis tools with respect to the probability of misclassification under binary classes....
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer International Publishing
2015
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4619473/ https://www.ncbi.nlm.nih.gov/pubmed/26523135 http://dx.doi.org/10.1186/s13637-015-0028-3 |
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author | Dalton, Lori A. Yousefi, Mohammadmahdi R. |
author_facet | Dalton, Lori A. Yousefi, Mohammadmahdi R. |
author_sort | Dalton, Lori A. |
collection | PubMed |
description | A recently proposed optimal Bayesian classification paradigm addresses optimal error rate analysis for small-sample discrimination, including optimal classifiers, optimal error estimators, and error estimation analysis tools with respect to the probability of misclassification under binary classes. Here, we address multi-class problems and optimal expected risk with respect to a given risk function, which are common settings in bioinformatics. We present Bayesian risk estimators (BRE) under arbitrary classifiers, the mean-square error (MSE) of arbitrary risk estimators under arbitrary classifiers, and optimal Bayesian risk classifiers (OBRC). We provide analytic expressions for these tools under several discrete and Gaussian models and present a new methodology to approximate the BRE and MSE when analytic expressions are not available. Of particular note, we present analytic forms for the MSE under Gaussian models with homoscedastic covariances, which are new even in binary classification. |
format | Online Article Text |
id | pubmed-4619473 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2015 |
publisher | Springer International Publishing |
record_format | MEDLINE/PubMed |
spelling | pubmed-46194732015-10-29 On optimal Bayesian classification and risk estimation under multiple classes Dalton, Lori A. Yousefi, Mohammadmahdi R. EURASIP J Bioinform Syst Biol Research A recently proposed optimal Bayesian classification paradigm addresses optimal error rate analysis for small-sample discrimination, including optimal classifiers, optimal error estimators, and error estimation analysis tools with respect to the probability of misclassification under binary classes. Here, we address multi-class problems and optimal expected risk with respect to a given risk function, which are common settings in bioinformatics. We present Bayesian risk estimators (BRE) under arbitrary classifiers, the mean-square error (MSE) of arbitrary risk estimators under arbitrary classifiers, and optimal Bayesian risk classifiers (OBRC). We provide analytic expressions for these tools under several discrete and Gaussian models and present a new methodology to approximate the BRE and MSE when analytic expressions are not available. Of particular note, we present analytic forms for the MSE under Gaussian models with homoscedastic covariances, which are new even in binary classification. Springer International Publishing 2015-10-24 /pmc/articles/PMC4619473/ /pubmed/26523135 http://dx.doi.org/10.1186/s13637-015-0028-3 Text en © Dalton and Yousefi. 2015 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
spellingShingle | Research Dalton, Lori A. Yousefi, Mohammadmahdi R. On optimal Bayesian classification and risk estimation under multiple classes |
title | On optimal Bayesian classification and risk estimation under multiple classes |
title_full | On optimal Bayesian classification and risk estimation under multiple classes |
title_fullStr | On optimal Bayesian classification and risk estimation under multiple classes |
title_full_unstemmed | On optimal Bayesian classification and risk estimation under multiple classes |
title_short | On optimal Bayesian classification and risk estimation under multiple classes |
title_sort | on optimal bayesian classification and risk estimation under multiple classes |
topic | Research |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4619473/ https://www.ncbi.nlm.nih.gov/pubmed/26523135 http://dx.doi.org/10.1186/s13637-015-0028-3 |
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