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UID:571@cran.univ-lorraine.fr
DTSTART;TZID=Europe/Paris:20241014T130000
DTEND;TZID=Europe/Paris:20241014T140000
DTSTAMP:20241011T104248Z
URL:https://www.cran.univ-lorraine.fr/events/seminaire-de-lucas-de-lara/
SUMMARY:Séminaire de Lucas De Lara
DESCRIPTION:Speaker: Lucas de Lara\, postdoctoral researcher at IECL/CRAN\n
 Title: On the nonconvexity of push-forward constraints and its consequence
 s in machine learning\nLocation: CRAN FST\, bâtiment Henri Poincaré\, 4
 ème étage\nAbstract:\nThe push-forward operation enables one to redistri
 bute a probability measure through a deterministic map. It plays a key rol
 e in statistics and optimization: many learning problems (notably from opt
 imal transport\, generative modeling\, and algorithmic fairness) include c
 onstraints or penalties framed as push-forward conditions on the model. Ho
 wever\, the literature lacks general theoretical insights on the (non)conv
 exity of such constraints and its consequences on the associated learning 
 problems. This work aims at filling this gap. In a first part\, we provide
  a range of sufficient and necessary conditions for the (non)convexity of 
 two sets of functions: the maps transporting one probability measure to an
 other\; the maps inducing equal output distributions across distinct proba
 bility measures. This highlights that for most probability measures\, thes
 e push-forward constraints are not convex. In a second time\, we show how 
 this result implies critical limitations on the design of convex optimizat
 ion problems for learning generative models or group-fair predictors. This
  work will hopefully help researchers and practitioners have a better unde
 rstanding of the critical impact of push-forward conditions onto convexity
 .
CATEGORIES:Département BioSiS,Séminaires projet SiMul
LOCATION:CRAN - FST - 4ème\, Campus Sciences\, Boulevard des Aiguillettes\
 , Vandoeuvre-lès-Nancy\, 54506\, France
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