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SUMMARY:Statistics and Geometry of Gromov-Wasserstein Distance - Bharath S
 riperumbudur (Pennsylvania State University)
DTSTART:20250508T104500Z
DTEND:20250508T114500Z
UID:TALK230482@talks.cam.ac.uk
DESCRIPTION:The Gromov-Wasserstein (GW) distance\, rooted in optimal trans
 port (OT) theory\, quantifies dissimilarity between metric measure spaces 
 and provides a natural framework for aligning them. As such\, GW distance 
 enables applications including object matching\, single-cell genomics\, an
 d matching language models. While computational aspects of the GW distance
  have been studied heuristically\, most of the mathematical theories about
  GW duality\, Brenier maps\, geometry\, etc.\, remained elusive\, despite 
 the rapid progress these aspects have seen under the classical OT paradigm
  in recent decades. This talk will cover recent progress on closing these 
 gaps for the GW. We present (i) sharp statistical estimation rates through
  duality\, (ii) a thorough investigation of the Jordan-Kinderlehrer-Otto (
 JKO) scheme for the gradient flow of inner product GW (IGW) distance\, and
  (iii) a dynamical formulation of IGW\, which generalizes the Benamou-Bren
 ier formula for the Wasserstein distance. Central to (ii) and (iii) is a R
 iemannian structure on the space of probability distributions\, based on w
 hich we also propose novel numerical schemes for measure evolution and def
 ormation. [Joint work with Zhengxin Zhang (Cornell)\, Ziv Goldfeld (Cornel
 l)\, Kristjan Greenewald (IBM Research)\, and Youssef Mroueh (IBM Research
 )]
LOCATION:Seminar Room 1\, Newton Institute
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