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SUMMARY:Statistical estimation of Monge transport maps with empirical Bren
 ier potentials
DTSTART:20260414T091500Z
DTEND:20260414T101500Z
DTSTAMP:20260410T104100Z
UID:indico-event-14477@indico.math.cnrs.fr
DESCRIPTION:Speakers: Edouard Pauwels (TSE)\n\nWe analyze a statistical es
 timator for Monge transport maps: solutions to the quadratic optimal trans
 port problem. For absolutely continuous source measures\, this map is uniq
 uely defined as the gradient of a convex function\, a result known as Bren
 ier theorem. Without absolute continuity\, the problem is relaxed\, maps a
 re replaced by coupling measures\, and optimal couplings are supported on 
 the subdifferential of a convex function: a Brenier potential. This charac
 terization is the basis for our Monge transport map estimator\, for measur
 es known only through finite samples. The resulting Brenier potential has 
 a simple closed form expression based on the dual solution of the discrete
  sampled problem. We exhibit convergence rates for this estimator based on
  a new error bound for the quadratic optimal transport problem. Our method
 ology does not rely on smoothness or continuity of the Monge transport map
  and requires no computation beyond primal-dual solutions of the discrete 
 finite dimensional linear program transport problem.\n\nhttps://indico.mat
 h.cnrs.fr/event/14477/
LOCATION:Salle K. Johnson (1R3\, 1er étage)
URL:https://indico.math.cnrs.fr/event/14477/
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