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Calibrated simplex-mapping classification

We propose a novel methodology for general multi-class classification in arbitrary feature spaces, which results in a potentially well-calibrated classifier. Calibrated classifiers are important in many applications because, in addition to the prediction of mere class labels, they also yield a confi...

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Detalles Bibliográficos
Autores principales: Heese, Raoul, Schmid, Jochen, Walczak, Michał, Bortz, Michael
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9844900/
https://www.ncbi.nlm.nih.gov/pubmed/36649243
http://dx.doi.org/10.1371/journal.pone.0279876
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author Heese, Raoul
Schmid, Jochen
Walczak, Michał
Bortz, Michael
author_facet Heese, Raoul
Schmid, Jochen
Walczak, Michał
Bortz, Michael
author_sort Heese, Raoul
collection PubMed
description We propose a novel methodology for general multi-class classification in arbitrary feature spaces, which results in a potentially well-calibrated classifier. Calibrated classifiers are important in many applications because, in addition to the prediction of mere class labels, they also yield a confidence level for each of their predictions. In essence, the training of our classifier proceeds in two steps. In a first step, the training data is represented in a latent space whose geometry is induced by a regular (n − 1)-dimensional simplex, n being the number of classes. We design this representation in such a way that it well reflects the feature space distances of the datapoints to their own- and foreign-class neighbors. In a second step, the latent space representation of the training data is extended to the whole feature space by fitting a regression model to the transformed data. With this latent-space representation, our calibrated classifier is readily defined. We rigorously establish its core theoretical properties and benchmark its prediction and calibration properties by means of various synthetic and real-world data sets from different application domains.
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spelling pubmed-98449002023-01-18 Calibrated simplex-mapping classification Heese, Raoul Schmid, Jochen Walczak, Michał Bortz, Michael PLoS One Research Article We propose a novel methodology for general multi-class classification in arbitrary feature spaces, which results in a potentially well-calibrated classifier. Calibrated classifiers are important in many applications because, in addition to the prediction of mere class labels, they also yield a confidence level for each of their predictions. In essence, the training of our classifier proceeds in two steps. In a first step, the training data is represented in a latent space whose geometry is induced by a regular (n − 1)-dimensional simplex, n being the number of classes. We design this representation in such a way that it well reflects the feature space distances of the datapoints to their own- and foreign-class neighbors. In a second step, the latent space representation of the training data is extended to the whole feature space by fitting a regression model to the transformed data. With this latent-space representation, our calibrated classifier is readily defined. We rigorously establish its core theoretical properties and benchmark its prediction and calibration properties by means of various synthetic and real-world data sets from different application domains. Public Library of Science 2023-01-17 /pmc/articles/PMC9844900/ /pubmed/36649243 http://dx.doi.org/10.1371/journal.pone.0279876 Text en © 2023 Heese et al https://creativecommons.org/licenses/by/4.0/This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
spellingShingle Research Article
Heese, Raoul
Schmid, Jochen
Walczak, Michał
Bortz, Michael
Calibrated simplex-mapping classification
title Calibrated simplex-mapping classification
title_full Calibrated simplex-mapping classification
title_fullStr Calibrated simplex-mapping classification
title_full_unstemmed Calibrated simplex-mapping classification
title_short Calibrated simplex-mapping classification
title_sort calibrated simplex-mapping classification
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9844900/
https://www.ncbi.nlm.nih.gov/pubmed/36649243
http://dx.doi.org/10.1371/journal.pone.0279876
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