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UID:239@isdm.umontpellier.fr
DTSTART;TZID=Europe/Paris:20240905T140000
DTEND;TZID=Europe/Paris:20240905T140000
DTSTAMP:20260825T134148Z
URL:https://isdm.umontpellier.fr/events/sparsistency-for-inverse-optimal-t
 ransport/
SUMMARY:Sparsistency for Inverse Optimal Transport
DESCRIPTION:Room 02.124\, Building 5\, St Priest campus\n\nMachine Learning
  in Montpellier\, Theory &amp\; Practice\n\nOptimal Transport is a useful 
 metric to compare probability distributions and to compute a pairing given
  a ground cost. Its entropic regularization variant (eOT) is crucial to ha
 ve fast algorithms and reflect fuzzy/noisy matchings. This work focuses on
  Inverse Optimal Transport (iOT)\, the problem of inferring the ground cos
 t from samples drawn from a coupling that solves an eOT problem. It is a r
 elevant problem that can be used to infer unobserved/missing links\, and t
 o obtain meaningful information about the structure of the ground cost yie
 lding the pairing. On one side\, iOT benefits from convexity\, but on the 
 other side\, being ill-posed\, it requires regularization to handle the sa
 mpling noise. This work presents an in-depth theoretical study of the l1 r
 egularization to model for instance Euclidean costs with sparse interactio
 ns between features. Specifically\, we derive a sufficient condition for t
 he robust recovery of the sparsity of the ground cost that can be seen as 
 a far reaching generalization of the Lasso's celebrated Irrepresentability
  Condition. To provide additional insight into this condition\, we work ou
 t in detail the Gaussian case. We show that as the entropic penalty varies
 \, the iOT problem interpolates between a graphical Lasso and a classical 
 Lasso\, thereby establishing a connection between iOT and graph estimation
 \, an important problem in ML.\n\nMachine Learning in Montpellier\, Theory
  &amp\; Practice
ATTACH;FMTTYPE=image/jpeg:https://isdm.umontpellier.fr/wp-content/uploads/
 2026/06/ml-mtp-gC78d5.png
CATEGORIES:ML MTP
LOCATION:Saint Priest Campus - Building 5 - Room 02.124\, 860 rue St Priest
 \, Montpellier\, 
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=860 rue St Priest\, Montpel
 lier\, ;X-APPLE-RADIUS=100;X-TITLE=Saint Priest Campus - Building 5 - Room
  02.124:geo:0,0
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