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CATEGORIES:Machine Learning Reading Group @ CUED
SUMMARY:Learning rates in Bayesian nonparametrics - Aad va
n der Vaart (Vrije Universiteit Amsterdam)
DTSTART;TZID=Europe/London:20091126T140000
DTEND;TZID=Europe/London:20091126T153000
UID:TALK19990AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/19990
DESCRIPTION:In semiparametric and nonparametric statistics the
unknown parameter is a function (e.g. regression
function\, density).\n\nA Bayesian method starts\,
as usual\, by the specification of a prior distri
bution on the parameter\, which is equivalent to m
odelling this function as a sample path of a stoch
astic process. Next Bayes' rule does the work and
comes up with the resulting posterior distribution
\, which is a probability distribution on a functi
on space.\n\nAfter giving examples of priors\, and
discussing the way prior and posterior can be vis
ualised\, we focus on studying the posterior distr
ibution under the (nonBayesian) assumption that th
e data is generated according to some fixed true d
istribution. We are interested in whether\, and i
f so how fast\, a sequence of posterior distributi
ons contracts to the true parameter if the amount
of data increases. We review general results and
examples\, including Gaussian process priors. The
general message is that\, unlike in parametric sta
tistics\, a prior often does not wash out\, and ha
s a big influence on the posterior.\n\nThis depend
ence may be alleviated by another round of prior m
odelling\, focused on a ``bandwidth'' parameter. T
he resulting hierarchical Bayesian procedures can
be viewed to provide an elegant and principled fra
mework for regularization and adaptation.\n
LOCATION:Engineering Department\, CBL Room 438
CONTACT:Shakir Mohamed
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