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SUMMARY:Sparsistency for inverse optimal transport - Clarice Poon (Univers
 ity of Warwick)
DTSTART:20231102T150000Z
DTEND:20231102T160000Z
UID:TALK207679@talks.cam.ac.uk
CONTACT:Georg Maierhofer
DESCRIPTION:Optimal Transport is a useful metric to compare probability di
 stributions and to compute a pairing given a ground cost. Its entropic reg
 ularization variant (eOT) is crucial to have fast algorithms and reflect f
 uzzy/noisy matchings. This work focuses on Inverse Optimal Transport (iOT)
 \, the problem of inferring the ground cost from samples drawn from a coup
 ling that solves an eOT problem. It is a relevant problem that can be used
  to infer unobserved/missing links\, and to obtain meaningful information 
 about the structure of the ground cost yielding the pairing. On one side\,
  iOT benefits from convexity\, but on the other side\, being ill-posed\, i
 t requires regularization to handle the sampling noise. This work presents
  a study of l1 regularization to model for instance Euclidean costs with s
 parse interactions between features.  Specifically\, we derive a sufficien
 t condition for the robust recovery of the sparsity of the ground cost tha
 t can be seen as a generalization of the Lasso’s celebrated ``Irrepresen
 tability Condition’’. To provide additional insight into this conditio
 n\, we consider the Gaussian case. We show that as the entropic penalty va
 ries\, the iOT problem interpolates between a graphical Lasso and a classi
 cal Lasso\, thereby establishing a connection between iOT and graph estima
 tion. This is joint work with Francisco Andrade and Gabriel Peyré.
LOCATION:Centre for Mathematical Sciences\, MR14
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