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CATEGORIES:Statistics
SUMMARY:Posterior concentration for Bayesian regression tr
ees and their ensembles - Stephanie van der Pas\,
University of Leiden
DTSTART;TZID=Europe/London:20181123T160000
DTEND;TZID=Europe/London:20181123T170000
UID:TALK109678AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/109678
DESCRIPTION:Since their inception in the 1980's\, regression t
rees have been one of the more widely used nonpara
metric prediction methods. Tree-structured methods
yield a histogram reconstruction of the regressio
n surface\, where the bins correspond to terminal
nodes of recursive partitioning. Trees are powerfu
l\, yet susceptible to overfitting. Strategies aga
inst overfitting have traditionally relied on prun
ing greedily grown trees. The Bayesian framework o
ffers an alternative remedy against overfitting th
rough priors. Roughly speaking\, a good prior char
ges smaller trees where overfitting does not occur
. In this paper\, we take a step towards understan
ding why/when do Bayesian trees and their ensemble
s not overfit. We study the speed at which the pos
terior concentrates around the true smooth regress
ion function. We propose a spike-and-tree variant
of the popular Bayesian CART prior and establish n
ew theoretical results showing that regression tre
es (and their ensembles) a) are capable of recover
ing smooth regression surfaces\, achieving optimal
rates up to a log factor\, b) can adapt to the un
known level of smoothness and c) can perform effec
tive dimension reduction. These results provide a
piece of missing theoretical evidence explaining w
hy Bayesian trees (and additive variants thereof)
have worked so well in practice.
LOCATION:MR12
CONTACT:Dr Sergio Bacallado
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