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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Optimal score estimation via empirical Bayes smoot
 hing - Andre Wibisono (Yale University)
DTSTART;TZID=Europe/London:20240715T160000
DTEND;TZID=Europe/London:20240715T170000
UID:TALK219025AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/219025
DESCRIPTION:We study the problem of estimating the score funct
 ion of an unknown probability distribution $\\rho^
 *$ from $n$ independent and identically distribute
 d observations in $d$ dimensions. Assuming that $\
 \rho^*$ is subgaussian and has a Lipschitz-continu
 ous score function $s^*$\, we establish the optima
 l rate of $\\tilde \\Theta(n^{-\\frac{2}{d+4}})$ f
 or this estimation problem under the loss function
  $\\|\\hat s - s^*\\|^2_{L^2(\\rho^*)}$ that is co
 mmonly used in the score matching literature\, hig
 hlighting the curse of dimensionality where sample
  complexity for accurate score estimation grows ex
 ponentially with the dimension $d$. Leveraging key
  insights in empirical Bayes theory as well as a n
 ew convergence rate of smoothed empirical distribu
 tion in Hellinger distance\, we show that a regula
 rized score estimator based on a Gaussian kernel a
 ttains this rate\, shown optimal by a matching min
 imax lower bound. We also discuss the implication 
 of our theory on the sample complexity of score-ba
 sed generative models. Joint work with Yihong Wu a
 nd Kaylee Yang.\n&nbsp\;
LOCATION:External
CONTACT:
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