The aim of this thesis is to propose new approaches based on non-additive integrals to construct explainable sparse models. In the last decade, an increasing attention was devoted to non-additive integrals, such as Choquet and Sugeno integrals, enabling to model interactions among variables and providing a fine control of synergies among them. They are more and more used in the context of supervised learning, i.e., where an algorithm has access to observations and their labels. The non-additive integrals are introduced into loss functions to learn reliable predictive models. In AI, the Choquet integral was successfully used to extend the logistic regression, and the Sugeno integral was applied to ordinal aggregation problems. In decision theory, these integrals are widely used to aggregate values attached to multiple interacting criteria while keeping a compact and interpretable model. In this thesis, we would like to take the best of the two worlds, machine learning and decision theory, both actively developed in Artificial Intelligence, to propose adaptive and interpretable evaluation models based on non-additive integrals and contribute to produce reliable predictive models. In particular, we are interested to efficiently optimise an objective (loss) function which is based on a compact Choquet integral.
PhD student: Margot Hérin
PhD supervisors: Patrice Perny, Nataliya Sokolovska
Research laboratory: Lip6