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SUMMARY:A Predictive Study of Bayesian Nonparametric Regression Models - S
 ara Wade\, Bocconi University
DTSTART:20120425T100000Z
DTEND:20120425T110000Z
UID:TALK37880@talks.cam.ac.uk
CONTACT:David Duvenaud
DESCRIPTION:In many situations\, the assumptions of the standard linear mo
 del are unreasonable due to the presence of non-linearity in the regressio
 n function and a non-normal error distribution that may evolve with x. Cou
 ntably infnite mixture models for the collection of conditional densities 
 provide a flexible tool that can capture such behavior. In this talk\, we 
 will review such models and discuss predictive issues that arise from diff
 erent choices of the covariate dependent weights and atoms. We will partic
 ularly focus on the model obtained  from a Dirichlet Process mixture model
  for the joint distribution of the response and covariate and examine the 
 impact of the dimension of the covariate\, p\, on prediction. We find that
  even for moderate p\, a large number of components will typically be used
  to estimate the predictive conditional density due to complexity of the m
 arginal of x. To address this issue\, we propose to replace the Dirichlet 
 Process with the Enriched Dirichlet Process. This allows for a more fexibl
 e local model for x\, leading to a smaller number of components and predic
 tive estimates within component to be based on larger sample sizes. The re
 sult is more reliable predictive estimates\, smaller credible intervals\, 
 and  less prior influence. Moreover\, computations are a simple extensions
  of those used for the Dirichlet Process mixture model. We demonstrate the
  advantages of our approach through a simulated example and an application
  to predict Alzheimer's Disease status.
LOCATION:Engineering Department\, CBL Room 438
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