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SUMMARY:Constrained and Localized Nonparametric Estimation and Optimizatio
 n - John Lafferty (U of Chicago)
DTSTART:20161104T160000Z
DTEND:20161104T170000Z
UID:TALK67489@talks.cam.ac.uk
CONTACT:Quentin Berthet
DESCRIPTION:We present work on two nonstandard frameworks for minimax anal
 ysis.\n\nFor the first problem\, imagine that I estimate a statistical mod
 el\nfrom data\, and then want to share my model with you. But we are\ncomm
 unicating over a resource constrained channel.  By sending lots of\nbits\,
  I can communicate my model accurately\, with little loss in\nstatistical 
 risk. Sending a small number of bits will incur some\nexcess risk.  What c
 an we say about the tradeoff between statistical\nrisk and the communicati
 on constraints?  This is a type of rate\ndistortion and constrained minima
 x problem\, for which we provide a\nsharp analysis in certain nonparametri
 c settings.\n\nThe second problem starts with the question "how difficult 
 is it to\nminimize a specific convex function?"  This is tricky to\nformal
 ize traditional complexity analysis is expressed in terms of\nthe worst ca
 se over a large class of instances.  We extend the\nclassical minimax anal
 ysis of stochastic convex optimization by\nintroducing a localized form of
  minimax complexity for individual\nfunctions. This uses a computational a
 nalogue of the modulus of\ncontinuity that is central to statistical minim
 ax analysis\, which\nserves as a computational analogue of Fisher informat
 ion.\n\nJoint work with Sabyasachi Chatterjee\, John Duchi\, and Yuancheng
  Zhu.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge.
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