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PRODID:-//Columba Systems Ltd//NONSGML CPNG/SpringViewer/ICal Output/3.3-
M3//EN
VERSION:2.0
CALSCALE:GREGORIAN
METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20240924T122711Z
DTSTART:20241002T140000Z
DTEND:20241002T150000Z
SUMMARY:SQUIDS Seminar - Linear Approximation and Manifold Learning in Op
timal Transport
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}xrp-m1gever
j-qffd55
DESCRIPTION:Abstract: Optimal transport distances are popular due to thei
r 'modelling assumptions'. But significant drawbacks such as a lack of o
ff-the-shelf data analysis tools and high computation cost limit their u
se in practice. The idea behind linear optimal transport is to define an
embedding from an optimal transport space to a Euclidean space that app
roximates the topology. We start the talk by reviewing this embedding fo
r the Wasserstein distance. Bounds on linear approximation are not parti
cularly good if the full Wasserstein space is considered. To better cont
rol the approximation we consider a submanifold of the Wasserstein space
and show one can get local linearisation of the same order as one expec
ts for Riemannian manifolds in Euclidean spaces. We finally consider lin
earisation in the Hellinger--Kantorovich space\, an extension of the Was
serstein distance to unbalanced measures. \n\nThis is joint work with Ti
anji Cai\, Junyi Cheng\, Keaton Hamm\, Caroline Moosemueller and Bernhar
d Schmitzer.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:G.113\, Alan Turing Building\, Manchester
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