Calibrated simplex-mapping classification

Raoul Heese, Jochen Schmid, Michał Walczak and Michael Bortz

PLOS ONE, 2023, vol. 18, issue 1, 1-26

Abstract: 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.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0279876

DOI: 10.1371/journal.pone.0279876

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