Learning Sets of Probabilities Through Ensemble Methods

A possible approach to obtain set-valued predictions is to learn for each query instance a probability set (a.k.a. credal set) representing its associated uncertainty. Theoretically founded decision rules extending classical expectation and inducing a partial order between predictions can the be used to derive set-valued predictions. However, obtaining such a credal set by imprecisiating a given learning algorithm is usually computationally challenging, except for simple models such as decision trees or naive Bayes classifiers. In this paper, we propose a simple, easy to use quantile-based framework for estimating credal sets using output of ensemble methods, that can also cope with complex types of data, such as images and mixed/multimodal data, etc. Experiments are conducted to highlight the usefulness of the proposed framework.