[2604.01939] Probabilistic classification from possibilistic data: computing Kullback-Leibler projection with a possibility distribution

Computer Science > Artificial Intelligence arXiv:2604.01939 (cs) [Submitted on 2 Apr 2026] Title:Probabilistic classification from possibilistic data: computing Kullback-Leibler projection with a possibility distribution Authors:Ismaïl Baaj, Pierre Marquis View a PDF of the paper titled Probabilistic classification from possibilistic data: computing Kullback-Leibler projection with a possibility distribution, by Isma\"il Baaj and Pierre Marquis View PDF HTML (experimental) Abstract:We consider learning with possibilistic supervision for multi-class classification. For each training instance, the supervision is a normalized possibility distribution that expresses graded plausibility over the classes. From this possibility distribution, we construct a non-empty closed convex set of admissible probability distributions by combining two requirements: probabilistic compatibility with the possibility and necessity measures induced by the possibility distribution, and linear shape constraints that must be satisfied to preserve the qualitative structure of the possibility distribution. Thus, classes with the same possibility degree receive equal probabilities, and if a class has a strictly larger possibility degree than another class, then it receives a strictly larger probability. Given a strictly positive probability vector output by a model for an instance, we compute its Kullback-Leibler projection onto the admissible set. This projection yields the closest admissible probabil...