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CATEGORIES:Statistics Reading Group
SUMMARY:Adaptive algorithms for Stratified Sampling Monte
Carlo - Alexandra Carpentier (Statistical Laborato
ry)
DTSTART;TZID=Europe/London:20130213T140000
DTEND;TZID=Europe/London:20130213T153000
UID:TALK41571AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/41571
DESCRIPTION:We consider the problem of estimating the integral
of a function f over a domain. Although no analyt
ic expression for f is available\, it is possible
to obtain n samples from f\, chosen anywhere in th
e domain. A popular method for computing the integ
ral of the function is to stratify the space in st
rata and sample points in the strata. \n\nWe prop
ose an algorithm for returning a stratified estima
te of the integral. We prove that this algorithm a
dapts online the number of samples in each stratum
to the amount of variation of the function in the
stratum. In particular\, this enables to allocate
more samples where the function varies more\, and
be almost as efficient as an "oracle" strategy th
at has access to the variations of the functions i
n each stratum. More precisions on this aspect is\
nin paper (Carpentier and Munos\, 2011). We also p
rovide some results on (i) how to choose the numbe
r of strata in an efficient way\nand (ii) how to a
dapt the strata themselves to the specific shape o
f the function. We express those results with fini
te-time bounds on a proxy of the variance of the e
stimate (returned by the algorithms we present).\n
LOCATION:MR9\, CMS
CONTACT:Robin Evans
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