Regression under Monotonicity and Fairness Constraints

par Mathis Deronzier

lundi 6 juil. 2026, 14:00 → 17:30 Europe/Paris

Amphithéâtre Laurent Schwartz, bâtiment 1R3 (Institut de Mathématiques de Toulouse)

For remote attendance, please use the following link: https://univ-lille-fr.zoom.us/j/93991989234?pwd=eN84HtcbCF2Kxwa0PDkuqjXFSe4K8R.1

The presentation will be given in English.

Composition of the comittee:

- Sébastien DA VEIGA, Reviewer, ENSAI
- Eustasio DEL BARRIO, Reviewer, University of Valladolid
- Béatrice LAURENT-BONNEAU, Examiner, INSA Toulouse
- Solenne GAUCHER, Examiner, Institut Polytechnique de Paris
- Didier RULLIÈRE, Examiner, Mines Saint-Étienne
- François BACHOC, PhD Supervisor, University of Lille
- Olivier ROUSTANT, Co-supervisor, INSA Toulouse
- Andrés F. López-Lopera, Co-supervisor, University of Montpellier

abstract:

This thesis studies the integration of functional constraints in regression problems, focusing on monotonicity and statistical parity (independence of predictions from the group-membership variable), through two complementary perspectives: constrained Gaussian processes and convex analysis.

It extends the framework of constrained Gaussian processes in two directions. The first generalizes existing models to block-additive structures, that is, sums of functions defined on disjoint subsets of the input variables. These structures enable applications to higher-dimensional problems while retaining a degree of flexibility. The second incorporates the statistical parity constraint into a Gaussian process and derives predictors that allow control of the trade-off between accuracy and fairness, as well as the degree of differential treatment between individuals. It establishes asymptotic properties of these predictors.

Then, it analyzes the geometric properties of the associated functional spaces. In particular, it establishes the non-convexity of the set of functions satisfying statistical parity, showing that no convex loss function can characterize this constraint and thereby ruling out the convex optimization framework. Finally, it exploits the convex cone structure of monotone functions to reformulate regression under monotonicity constraints via convex duality. More precisely, the characterization of the dual cone of monotone functions opens up a new approach to this problem.