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SUMMARY:An optimal unrestricted learning procedure - Shahar Mendelson (Tec
 hnion - Israel Institute of Technology\; Australian National University)
DTSTART:20180119T110000Z
DTEND:20180119T114500Z
UID:TALK97906@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The question of prediction is of central importance in Statist
 ical Learning Theory. The optimal tradeoff between accuracy and confidence
  and the identity of a procedure that attains that optimal tradeoff have b
 een studied extensively over the years.<br><br>In this talk I present some
  of ideas used in the recent solution of this problem: a procedure $\\hat{
 f}$ that attains the best possible accuracy/confidence tradeoff for a trip
 let $(F\,X\,Y)$ consisting of an arbitrary class $F$\, an unknown distribu
 tion $X$ and an unknown target $Y$.<br><br>Specifically\, I explain why un
 der minimal assumptions on $(F\,X\,Y)$\, there is a natural critical level
  $r^*$ that depends on the triplet and the sample size $N$\, such that for
  any accuracy parameter $r>r^*$\, one has $E((\\hat{f}(X)-Y)^2|D) \\leq \\
 inf_{f \\in F} E(f(X)-Y)^2+r^2$ with probability at least $1-2\\exp(-cN \\
 min\\{1\,r^2/\\sigma^2\\})$\,<br>where $\\sigma^2=\\inf_{f \\in F} E(f(X)-
 Y)^2$.
LOCATION:Seminar Room 1\, Newton Institute
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