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CATEGORIES:Machine Learning Reading Group @ CUED
SUMMARY:A Predictive Study of Bayesian Nonparametric Regre
ssion Models - Sara Wade\, Bocconi University
DTSTART;TZID=Europe/London:20120425T110000
DTEND;TZID=Europe/London:20120425T120000
UID:TALK37880AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/37880
DESCRIPTION:In many situations\, the assumptions of the standa
rd linear model are unreasonable due to the presen
ce of non-linearity in the regression function and
a non-normal error distribution that may evolve w
ith x. Countably infnite mixture models for the co
llection of conditional densities provide a flexib
le tool that can capture such behavior. In this ta
lk\, we will review such models and discuss predic
tive issues that arise from different choices of t
he covariate dependent weights and atoms. We will
particularly focus on the model obtained from a D
irichlet Process mixture model for the joint distr
ibution 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 us
ed to estimate the predictive conditional density
due to complexity of the marginal of x. To address
this issue\, we propose to replace the Dirichlet
Process with the Enriched Dirichlet Process. This
allows for a more fexible local model for x\, lead
ing to a smaller number of components and predicti
ve estimates within component to be based on large
r sample sizes. The result is more reliable predic
tive estimates\, smaller credible intervals\, and
less prior influence. Moreover\, computations are
a simple extensions of those used for the Dirichl
et Process mixture model. We demonstrate the advan
tages of our approach through a simulated example
and an application to predict Alzheimer's Disease
status.
LOCATION:Engineering Department\, CBL Room 438
CONTACT:David Duvenaud
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