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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:The remarkable flexibility of BART - Edward George
(University of Pennsylvania )
DTSTART;TZID=Europe/London:20180530T100000
DTEND;TZID=Europe/London:20180530T110000
UID:TALK106351AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/106351
DESCRIPTION:For the canonical regression setup where one wants
to discover the relationship between Y and a p-di
mensional vector x\, BART (Bayesian Additive Regre
ssion Trees) approximates the conditional mean E[Y
|x] with a sum of regression trees model\, where e
ach tree is constrained by a regularization prior
to be a weak learner. Fitting and inference are ac
complished via a scalable iterative Bayesian backf
itting MCMC algorithm that generates samples from
a posterior. Effectively\, BART is a nonparametric
Bayesian regression approach which uses dimension
ally adaptive random basis elements. Motivated by
ensemble methods in general\, and boosting algorit
hms in particular\, BART is defined by a statistic
al model: a prior and a likelihood. This approach
enables full posterior inference including point a
nd interval estimates of the unknown regression fu
nction as well as the marginal effects of potentia
l predictors. By keeping track of predictor inclus
ion frequencies\, BART can also be used for model-
free variable selection. To further illustrate the
modeling flexibility of BART\, we introduce two e
laborations\, MBART and HBART. Exploiting the pote
ntial monotonicity of E[Y|x] in components of x\,
MBART incorporates such monotonicity with a multiv
ariate basis of monotone trees\, thereby enabling
estimation of the decomposition of E[Y|x] into its
unique monotone components. To allow for the poss
ibility of heteroscedasticity\, HBART incorporates
an additional product of regression trees model c
omponent for the conditional variance\, thereby pr
oviding simultaneous inference about both E[Y|x] a
nd Var[Y|x]. (This is joint research with Hugh Chi
pman\, Matt Pratola\, Rob McCulloch and Tom Shivel
y.)

LOCATION:Seminar Room 2\, Newton Institute
CONTACT:info@newton.ac.uk
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