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SUMMARY:The remarkable flexibility of BART - Edward George (University of 
 Pennsylvania )
DTSTART:20180530T090000Z
DTEND:20180530T100000Z
UID:TALK107242@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:For the canonical regression setup where one wants to discover
  the relationship between Y and a p-dimensional vector x\, BART (Bayesian 
 Additive Regression Trees) approximates the conditional mean E[Y|x] with a
  sum of regression trees model\, where each tree is constrained by a regul
 arization prior to be a weak learner. Fitting and inference are accomplish
 ed via a scalable iterative Bayesian backfitting MCMC algorithm that gener
 ates samples from a posterior. Effectively\, BART is a nonparametric Bayes
 ian regression approach which uses dimensionally adaptive random basis ele
 ments. Motivated by ensemble methods in general\, and boosting algorithms 
 in particular\, BART is defined by a statistical model: a prior and a like
 lihood. This approach enables full posterior inference including point and
  interval estimates of the unknown regression function as well as the marg
 inal effects of potential 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
  elaborations\, MBART and HBART. Exploiting the potential monotonicity of 
 E[Y|x] in components of x\, MBART incorporates such monotonicity with a mu
 ltivariate basis of monotone trees\, thereby enabling estimation of the de
 composition of E[Y|x] into its unique monotone components. To allow for th
 e possibility of heteroscedasticity\, HBART incorporates an additional pro
 duct of regression trees model component for the conditional variance\, th
 ereby providing simultaneous inference about both E[Y|x] and Var[Y|x]. (Th
 is is joint research with Hugh Chipman\, Matt Pratola\, Rob McCulloch and 
 Tom Shively.)  <br><br><br><br><br>
LOCATION:Seminar Room 2\, Newton Institute
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