Extrapolation of the Bayesian classifier with an unknown support of the two-class mixture distribution

K. S. Lukyanov ; P. A. Yaskov ; A. I. Perminov ; A. P. Kovalenko ; D. Y. Turdakov

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 79 (2024) no. 6, pp. 991-1015

Résumé

This work introduces a method aimed at enhancing the reliability of the Bayesian classifier. The method involves augmenting the training dataset, which consists of a mixture of distributions from two original classes, with artificially generated observations from a third, ‘background’ class, uniformly distributed over a compact set that contains the unknown support of the original mixture. This modification allows the value of the discriminant function outside the support of the training data distribution to approach a prescribed level (in this case, zero). Adding a decision option for ‘Refusal to Classify’, triggered when the discriminant function takes sufficiently small values, results in a localized increase in classifier reliability. Specifically, this approach addresses several issues: it enables the rejection of data that differs significantly from the training data; facilitates the detection of anomalies in input data; and avoids decision-making in ‘boundary’ regions when separating classes. The paper provides a theoretical justification for the optimality of the proposed classifier. The practical utility of the method is demonstrated through classification tasks involving images and time series. Additionally, a methodology for identifying trusted regions is proposed. This methodology can be used to detect anomalous data, cases of parameter shifts in class distributions, and areas of overlap between the distributions of the original classes. Based on these trusted regions, quantitative metrics for classifier reliability and efficiency are introduced. Bibliography: 23 titles.

Détail

Keywords: machine learning, Bayesian classifier, trusted machine learning, interpretability, out-of-distribution (OOD), time series classification, rejection of classification, background class.
Mots-clés : image classification