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CATEGORIES:Academics,Lectures/Seminars
DESCRIPTION:Abstract: Optimal Transport\, a theory for optimal allocation o
f resources\, is widely used in various fields such as astrophysics\, machi
ne learning\, and imaging science. However\, many applications impose eleme
ntwise constraints on the transport plan which traditional optimal transpor
t cannot enforce. Here we introduce Supervised Optimal Transport (sOT) that
formulates a constrained optimal transport problem where couplings between
certain elements are prohibited according to specific applications. sOT is
proved to be equivalent to an $l^1$ penalized optimization problem\, from
which efficient algorithms are designed to solve its entropy regularized fo
rmulation. We demonstrate the capability of sOT by comparing it to other va
riants and extensions of traditional OT in color transfer problem. We also
study the barycenter problem in sOT formulation\, where we discover and pro
ve a unique reverse and portion selection (control) mechanism. Supervised o
ptimal transport is broadly applicable to applications in which constrained
transport plan is involved and the original unit should be preserved by av
oiding normalization.\n\n \n\nDr Yanxiang Zhao has been an associate profes
sor in the department of mathematics at George Washington University since
2019. He holds a Ph.D in mathematics from Pennsylvania state university (20
11). Before he went to Washington in 2014\, he worked as a postdoc at the d
epartment of mathematics\, University of California\, San Diego. His resear
ch interests include Mathematical modeling and applications in biology\, ph
ysics and computer science\; Computational mathematics. Specifically\, he i
s working on phase field or diffuse interface approach for the modeling and
simulations of some interfacial problems and phase field based variational
implicit-solvent models for biomolecular interactions. Dr. Zhao has receiv
ed a number of award including GWU University Facilitating Fund Award and
Simons Collaboration Grants for Mathematicians.
DTEND:20211112T190000Z
DTSTAMP:20220516T212824Z
DTSTART:20211112T180000Z
LOCATION:
SEQUENCE:0
SUMMARY:Supervised Optimal Transport
UID:tag:localist.com\,2008:EventInstance_38306465291921
URL:https://events.mtu.edu/event/supervised_optimal_transport
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