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SUMMARY:CDM-Seminars - Gromov-Wasserstein distances between finite spaces:
  Duality\, computation\, and entropic approximation
DTSTART:20260402T143000
DTEND:20260402T160000
DTSTAMP:20260922T004543Z
UID:240c4b6472f2fbd585d97fc3c5a6b3bfb17ef58b7b904095da5d4f17
CATEGORIES:Conferences - Seminars
DESCRIPTION:Professor Gabriel RIOUX\n\nImperial College London\nAbstract:\
 nIn recent years\, the study of computational optimal transport (OT) has a
 dvanced significantly\, driven\, in part\, by its broad applicability acro
 ss data science\, statistics\, economics\, and physics. While OT distances
 \, such as the Wasserstein metric\, are well suited for comparing distribu
 tions on the same space and endow the space of probabilities on a given sp
 ace with a rich geometry\, comparing datasets of different types -- such a
 s text and images -- requires specifying an ad hoc cost function\, which m
 ay fail to capture a meaningful correspondence between datasets. \n\nTo a
 ddress this limitation\, Gromov-Wasserstein (GW) distances have been propo
 sed as a natural extension of the OT framework for comparing metric measur
 e (mm) spaces based only on their intrinsic structure. Notably\, GW distan
 ces define a metric on the space of all mm spaces and provide a means by w
 hich to align them. Despite their broad applicability to comparing heterog
 eneous datasets\, the computational study of GW distances remains limited.
  In effect\, even the entropically regularized GW problem\, most commonly 
 used by practitioners as an efficient proxy for the true GW problem\, was 
 only recently shown to admit algorithms subject to non-asymptotic converge
 nce rates albeit for Euclidean mm spaces. \n\nThis talk will outline rece
 nt progress in computational GW. Notably\, we furnish a new variational fo
 rmulation for the GW problem between finite mm spaces which naturally lead
 s to new algorithms for solving this problem with and without entropic reg
 ularization. As a consequence of this analysis\, we show that\, under cert
 ain conditions\, the iterates of our proposed method coincide with those o
 f a variant of the mirror descent solver\, which is the most popular regul
 arized GW solver\, allowing us to prove the first non-asymptotic convergen
 ce rates for that approach. Furthermore\, we establish that solutions of t
 he entropic GW converge to solutions of the standard GW problem at an expo
 nential rate once the underlying quadratic program is concave\, but that t
 his rate is as slow as quadratic otherwise.\n \nThis is joint work with Z
 iv Goldfeld\, Riccardo Passeggeri\, and their students\, Venkatkrishna Kar
 umanchi and Joanna Marks.\n\n\nReferences:\n\nShort bio:  Gabriel is a Ch
 apman fellow in statistics at Imperial College London's Department of Math
 ematics. He obtained his Ph.D. In Applied Mathematics from Cornell Univers
 ity working under the supervision of Prof. Ziv Goldfeld. His main research
  interests lie in optimization\, mathematical statistics\, and probability
 \; he is particularly interested in the interplay between these topics wit
 hin the context of optimal transport theory. His work is supported in part
  by a postgraduate fellowship from the National Science and Engineering R
 esearch Council of Canada (NSERC). \n\nMore information about the speaker
 \n 
LOCATION:ODY 4 03 https://plan.epfl.ch/?room==ODY%204%2003 https://epfl.zo
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STATUS:CONFIRMED
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