Sparsistency for inverse optimal transport

Add to your list(s) Download to your calendar using vCal

• Clarice Poon (University of Warwick)
• Thursday 02 November 2023, 15:00-16:00
• Centre for Mathematical Sciences, MR14.

If you have a question about this talk, please contact Georg Maierhofer.

Optimal 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 have fast algorithms and reflect fuzzy/noisy matchings. This work focuses on Inverse Optimal Transport (iOT), the problem of inferring the ground cost from samples drawn from a coupling 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, it requires regularization to handle the sampling noise. This work presents a study of l1 regularization to model for instance Euclidean costs with sparse interactions between features. Specifically, we derive a sufficient condition for the robust recovery of the sparsity of the ground cost that can be seen as a generalization of the Lasso’s celebrated ``Irrepresentability Condition’’. To provide additional insight into this condition, we consider 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. This is joint work with Francisco Andrade and Gabriel Peyré.

This talk is part of the Applied and Computational Analysis series.

This talk is included in these lists:

• All CMS events
• All Talks (aka the CURE list)
• Applied and Computational Analysis
• CMS Events
• Centre for Mathematical Sciences, MR14
• DAMTP info aggregator
• Featured lists
• Interested Talks
• My seminars
• Type the title of a new list here
• bld31

Note that ex-directory lists are not shown.