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SUMMARY:Regression under Monotonicity and Fairness Constraints
DTSTART:20260706T120000Z
DTEND:20260706T153000Z
DTSTAMP:20260707T001900Z
UID:indico-event-16875@indico.math.cnrs.fr
DESCRIPTION:Speakers: Mathis Deronzier\n\nFor remote attendance\, please u
 se the following link: https://univ-lille-fr.zoom.us/j/93991989234?pwd=eN8
 4HtcbCF2Kxwa0PDkuqjXFSe4K8R.1 The presentation will be given in English. C
 omposition of the comittee: - Sébastien DA VEIGA\, Reviewer\, ENSAI - Eus
 tasio DEL BARRIO\, Reviewer\, University of Valladolid - Béatrice LAURENT
 -BONNEAU\, Examiner\, INSA Toulouse - Solenne GAUCHER\, Examiner\, Institu
 t Polytechnique de Paris - Didier RULLIÈRE\, Examiner\, Mines Saint-Étie
 nne - François BACHOC\, PhD Supervisor\, University of Lille - Olivier RO
 USTANT\, Co-supervisor\, INSA Toulouse - Andrés F. López-Lopera\, Co-sup
 ervisor\, University of Montpellier abstract: This thesis studies the inte
 gration of functional constraints in regression problems\, focusing on mon
 otonicity and statistical parity (independence of predictions from the gro
 up-membership variable)\, through two complementary perspectives: constrai
 ned Gaussian processes and convex analysis. It extends the framework of co
 nstrained Gaussian processes in two directions. The first generalizes exis
 ting models to block-additive structures\, that is\, sums of functions def
 ined on disjoint subsets of the input variables. These structures enable a
 pplications to higher-dimensional problems while retaining a degree of fle
 xibility. The second incorporates the statistical parity constraint into a
  Gaussian process and derives predictors that allow control of the trade-o
 ff between accuracy and fairness\, as well as the degree of differential t
 reatment between individuals. It establishes asymptotic properties of thes
 e predictors. Then\, it analyzes the geometric properties of the associate
 d functional spaces. In particular\, it establishes the non-convexity of t
 he 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 stru
 cture of monotone functions to reformulate regression under monotonicity c
 onstraints via convex duality. More precisely\, the characterization of th
 e dual cone of monotone functions opens up a new approach to this problem.
 \n\nhttps://indico.math.cnrs.fr/event/16875/
LOCATION:Amphithéâtre Laurent Schwartz\, bâtiment 1R3 (Institut de Math
 ématiques de Toulouse)
URL:https://indico.math.cnrs.fr/event/16875/
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