One of the most common and studied problem in machine learning is classification. While conventional algorithms for supervised classification rely on the determination of a function from features to labels, we propose a different approach based on the estimation of a probabilistic transformation from features to labels. Indeed, we determine a conditional probability distribution of the labels given the features and then features are classified as labels following such distribution. In order to compute the conditional distribution, we follow a robust minimax approach, minimizing the worst-case expectation of the 0-1 loss. By doing so, we find the probabilistic transformation which achieves the minimum risk against an uncertainty set consistent with the training data. We show numerical results obtained by an implementation in python of this method and we compare its performance with state of the art techniques.

Different types of training data have led to numerous schemes for supervised classification. Current learning techniques are tailored to one specific scheme and cannot handle general ensembles of training data. This paper presents a unifying framework for supervised classification with general ensembles of training data, and proposes the learning methodology of generalized robust risk minimization (GRRM). The paper shows how current and novel supervision schemes can be addressed under the proposed framework by representing the relationship between examples at test and training via probabilistic transformations. The results show that GRRM can handle different types of training data in a unified manner, and enable new supervision schemes that aggregate general ensembles of training data.

Abstract-- In this paper, we propose in Dezert-Smarandache Theory (DSmT) framework, a new probabilistic transformation, called DSmP, in order to build a subjective probability measure from any basic belief assignment defined on any model of the frame of discernment. Several examples are given to show how the DSmP transformation works and we compare it to main existing transformations proposed in the literature so far. We show the advantages of DSmP over classical transformations in term of Probabilistic Information Content (PIC). The direct extension of this transformation for dealing with qualitative belief assignments is also presented. In the theories of belief functions, Dempster-Shafer Theory (DST) [4], Transferable Belief Model (TBM) [11] or DSmT [6], [7], the mapping from the belief to the probability domain is a controversial issue.