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SUMMARY:Improved performance guarantees for Tukey’s median - Stanislav M
 insker (University of Southern California)
DTSTART:20250502T130000Z
DTEND:20250502T140000Z
UID:TALK231160@talks.cam.ac.uk
CONTACT:Qingyuan Zhao
DESCRIPTION:Is there a natural way to order data in dimension greater than
  one? The approach based on the notion of half-space depth\, often associa
 ted with the name of John Tukey\, is among the most popular. Tukey’s dep
 th has found applications in robust statistics\, the study of elections an
 d social choice\, and graph theory. We will give an introduction to the to
 pic\, with an emphasis on robust statistics\, describe some remaining open
  questions as well as our recent progress towards their solutions. In will
  particular\, we discuss performance guarantees for Tukey’s median (and 
 other affine-equivariant estimators) that depend on the “intrinsic” di
 mension of the problem expressed via the effective rank of the covariance 
 matrix\, and their connections to the size of empirical depth level sets.\
 n\nThis talk is based on the joint work with Yinan Shen.
LOCATION:MR12\, Centre for Mathematical Sciences
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