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CATEGORIES:Statistics
SUMMARY:Constrained and Localized Nonparametric Estimation
and Optimization - John Lafferty (U of Chicago)
DTSTART;TZID=Europe/London:20161104T160000
DTEND;TZID=Europe/London:20161104T170000
UID:TALK67489AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/67489
DESCRIPTION:We present work on two nonstandard frameworks for
minimax analysis.\n\nFor the first problem\, imagi
ne that I estimate a statistical model\nfrom data\
, and then want to share my model with you. But we
are\ncommunicating over a resource constrained ch
annel. By sending lots of\nbits\, I can communica
te my model accurately\, with little loss in\nstat
istical risk. Sending a small number of bits will
incur some\nexcess risk. What can we say about th
e tradeoff between statistical\nrisk and the commu
nication constraints? This is a type of rate\ndis
tortion and constrained minimax problem\, for whic
h we provide a\nsharp analysis in certain nonparam
etric settings.\n\nThe second problem starts with
the question "how difficult is it to\nminimize a s
pecific convex function?" This is tricky to\nform
alize traditional complexity analysis is expressed
in terms of\nthe worst case over a large class of
instances. We extend the\nclassical minimax anal
ysis of stochastic convex optimization by\nintrodu
cing a localized form of minimax complexity for in
dividual\nfunctions. This uses a computational ana
logue of the modulus of\ncontinuity that is centra
l to statistical minimax analysis\, which\nserves
as a computational analogue of Fisher information.
\n\nJoint work with Sabyasachi Chatterjee\, John D
uchi\, and Yuancheng Zhu.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberfo
rce Road\, Cambridge.
CONTACT:Quentin Berthet
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