Discrete Box-Constrained Minimax Classifier for Uncertain and Imbalanced Class Proportions

Cyprien Gilet (1) , Susana Barbosa (2) , Lionel Fillatre (3)

1 I3S - Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis
2 IPMC - Institut de pharmacologie moléculaire et cellulaire
3 Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Projet MEDIACODING

The goal of this paper is to build a supervised classifier addressing the following difficulties which commonly appear in safety-critical applications: imbalanced datasets, uncertain class proportions, dependencies between some features, presence of both numeric and categorical features, and arbitrary loss functions provided by experts. Many works have shown that discretizing the numeric features is relevant for dealing with mixed attributes. Thus, we develop a novel minimax classifier algorithm, designed for processing discrete or discretized features, which addresses all the previously mentioned issues. The usual minimax criterion derives from the computation of the class proportions which maximize the empirical Bayes risk over the probabilistic simplex. However, it can be potentially too pessimistic when the least favorable priors appear unrealistic or its risk of error becomes too high. In this case, under the assumption that the experts are able to provide independent bounds on some class proportions, our approach takes into account these constraints to decrease the risk of error. The resulting box-constrained minimax classifier appears as a trade-off between the discrete Bayes classifier and the usual minimax classifier.

Mots clés: Minimax Classifier; Γ-Minimax Classifier; Imbalanced datasets; Uncertain Class Proportions; Discrete Bayes Classifier; Histogram Rule; Bayesian Robustness

Domaines: Machine Learning [stat.ML]; Optimisation et contrôle [math.OC]; Statistiques [math.ST]

Cyprien Gilet, Susana Barbosa, Lionel Fillatre. Discrete Box-Constrained Minimax Classifier for Uncertain and Imbalanced Class Proportions. 2020. ⟨hal-02296592v2⟩