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SUMMARY:Entropic optimal transport: stability\, limit theorems\, and algor
 ithms - Kengo Kato (Cornell University)
DTSTART:20231117T140000Z
DTEND:20231117T150000Z
UID:TALK206020@talks.cam.ac.uk
CONTACT:Qingyuan Zhao
DESCRIPTION:In this talk\, I will discuss my recent work on entropic optim
 al transport (EOT). In the first part\, I will discuss limit theorems for 
 EOT maps\, dual potentials\, and the Sinkhorn divergence. The key technica
 l tool we use is a first and second-order Hadamard differentiability analy
 sis of EOT potentials with respect to the marginal distributions\, from wh
 ich the limit theorems\, bootstrap consistency\, and asymptotic efficiency
  of the empirical estimators follow. The second part concerns the entropic
  Gromov-Wasserstein (EGW) distance\, which serves as a computationally eff
 icient proxy for the Gromov-Wasserstein distance. By leveraging a variatio
 nal representation that ties the EGW problem with a series of EOT problems
 \, we derive stability results of EGW with respect to the auxiliary matrix
 \, which enables us to develop efficient algorithms for solving the EGW pr
 oblem. This talk is based on joint work with Ziv Goldfeld\, Gabriel Rioux\
 , and Ritwik Sadhu.
LOCATION:MR12\, Centre for Mathematical Sciences
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