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Calibrated simplex-mapping classification

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  • Raoul Heese
  • Jochen Schmid
  • Michał Walczak
  • Michael Bortz

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.

Suggested Citation

  • Raoul Heese & Jochen Schmid & Michał Walczak & Michael Bortz, 2023. "Calibrated simplex-mapping classification," PLOS ONE, Public Library of Science, vol. 18(1), pages 1-26, January.
  • Handle: RePEc:plo:pone00:0279876
    DOI: 10.1371/journal.pone.0279876
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