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SUMMARY:Minimax estimation of smooth densities in Wasserstein distance - J
 onathan Niles-Weed (Courant Institute)
DTSTART:20201106T160000Z
DTEND:20201106T170000Z
UID:TALK152557@talks.cam.ac.uk
CONTACT:Dr Sergio Bacallado
DESCRIPTION:We study nonparametric density estimation problems where error
  is measured in the Wasserstein distance\, a metric on probability distrib
 utions popular in many areas of statistics and machine learning. We give t
 he first minimax-optimal rates for this problem for general Wasserstein di
 stances\, and show that\, unlike classical nonparametric density estimatio
 n\, these rates depend on whether the densities in question are bounded be
 low. Motivated by variational problems involving the Wasserstein distance\
 , we also show how to construct discretely supported measures\, suitable f
 or computational purposes\, which achieve the minimax rates. Our main tech
 nical tool is an inequality giving a nearly tight dual characterization of
  the Wasserstein distances in terms of Besov norms. \n\nJoint work with Q.
  Berthet.
LOCATION: https://maths-cam-ac-uk.zoom.us/j/92821218455?pwd=aHFOZWw5bzVReU
 NYR2d5OWc1Tk15Zz09
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