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SUMMARY:FLAIR external seminar: New statistical phenomena for entropic opt
 imal transport
DTSTART:20230424T131500
DTSTAMP:20260524T152303Z
UID:cfff5755bd51f0e840f18082aef4fffdc3aeea2279f8fbfd45009377
CATEGORIES:Conferences - Seminars
DESCRIPTION:Austin J. Stromme\nTitle: New statistical phenomena for entr
 opic optimal transport\n\nSpeaker: Austin J. Stromme (MIT) \n\nAbstract
 : Optimal transport (OT) is a popular framework for comparing and interpo
 lating probability measures\, which has recently been used in diverse appl
 ication areas throughout science\, including in generative modeling\, cell
 ular biology\, graphics\, and beyond. Unfortunately\, recent work has show
 n that OT suffers from a severe statistical curse of dimensionality. In pr
 actice\, however\, the un-regularized OT problem is less common than entro
 pically regularized approximations\, known as entropic OT\, which afford t
 he use of simpler and more scalable algorithms.\n\nMotivated by its ubiqui
 ty in practice\, as well as the curse of dimensionality for its un-regular
 ized counterpart\, in this talk we identify two new statistical phenomena 
 for entropic OT in the form of bounds on the convergence rate of empirical
  quantities to their population counterparts. Our first set of bounds are 
 for high-dimensional settings\, and give totally dimension-free convergenc
 e\, albeit with exponential dependence on the regularization parameter. An
 d our second set of bounds are for data distributions with potentially sma
 ll intrinsic dimension\, in which case we show that the dimension-dependen
 ce is not only intrinsic to the data distributions\, but in fact is automa
 tically the minimum of the intrinsic dimensions of the two distributions a
 t stake. We show that these phenomena hold for entropic OT value estimatio
 n\, and more generally for the problems of entropic OT map and density est
 imation. We conclude with applications to transfer learning and trajectory
  reconstruction. Our simple proof techniques are inspired by convex optimi
 zation\, and notably avoid empirical process theory almost entirely.\n\nBa
 sed on joint work with Philippe Rigollet.
LOCATION:GA 3 21 https://plan.epfl.ch/?room==GA%203%2021
STATUS:CONFIRMED
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