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DTSTAMP:20250916T201819Z
DESCRIPTION:Sample-Efficient Learning of Mixture Distributions.\n\nLearning
  about a probability distribution from a sample generated by that distribu
 tion is a fundamental task. We consider PAC learning of probability distri
 butions (a.k.a. density estimation)\, where we are given an i.i.d. sample 
 generated from an unknown target distribution\, and want to output a distr
 ibution that is close to the target. Given the target distribution can be 
 approximated by a member of some predetermined class of distributions\, we
  analyze how large should a sample be so that one is able to find a distri
 bution that is close to the target in total variation distance.  Determini
 ng such sample complexity with respect to an arbitrary class of distributi
 ons is a fundamental open problem.\n	\n	In particular\, we improve the best 
 known upper bounds for learning a variety of mixture classes\, including m
 ixtures of Gaussian distributions over R^n. Furthermore\, we introduce a n
 ovel method for learning distributions via a form of compression. Using th
 is generic framework\, we provide the first tight bound (up to logarithmic
  factors) for learning the class of mixtures of axis-aligned Gaussians. Th
 is is joint work with Abbas Mehrabian and Shai Ben-David.Learning about a 
 probability distribution from a sample generated by that distribution is a
  fundamental task. We consider PAC learning of probability distributions (
 a.k.a. density estimation)\, where we are given an i.i.d. sample generated
  from an unknown target distribution\, and want to output a distribution t
 hat is close to the target. Given the target distribution can be approxima
 ted by a member of some predetermined class of distributions\, we analyze 
 how large should a sample be so that one is able to find a distribution th
 at is close to the target in total variation distance.  Determining such s
 ample complexity with respect to an arbitrary class of distributions is a 
 fundamental open problem.\n	\n	In particular\, we improve the best known upp
 er bounds for learning a variety of mixture classes\, including mixtures o
 f Gaussian distributions over R^n. Furthermore\, we introduce a novel meth
 od for learning distributions via a form of compression. Using this generi
 c framework\, we provide the first tight bound (up to logarithmic factors)
  for learning the class of mixtures of axis-aligned Gaussians. This is joi
 nt work with Abbas Mehrabian and Shai Ben-David.\n
DTSTART:20171206T150000Z
DTEND:20171206T160000Z
LOCATION:Room 1205\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Hassan Ashtiani\, University of Waterloo
URL:/mathstat/channels/event/hassan-ashtiani-universit
 y-waterloo-283164
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