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CATEGORIES:Statistics
SUMMARY:Model Selection in High-Dimensional Misspecified M
odels - Yang Feng\, Columbia University
DTSTART;TZID=Europe/London:20141205T160000
DTEND;TZID=Europe/London:20141205T170000
UID:TALK54678AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/54678
DESCRIPTION:Model selection is indispensable to high-dimension
al sparse modeling in selecting the best set of co
variates among a sequence of candidate models. Mos
t existing work assumes implicitly that the model
is correctly specified or of fixed dimensions. Yet
model misspecification and high dimensionality ar
e common in real applications. In this paper\, we
investigate two classical Kullback-Leibler diverge
nce and Bayesian principles of model selection in
the setting of high-dimensional misspecified model
s. Asymptotic expansions of these principles revea
l that the effect of model misspecification is cru
cial and should be taken into account\, leading to
the generalized AIC and generalized BIC in high d
imensions. With a natural choice of prior probabil
ities\, we suggest the generalized BIC with prior
probability which involves a logarithmic factor of
the dimensionality in penalizing model complexity
. We further establish the consistency of the cova
riance contrast matrix estimator in a general sett
ing. Our results and new method are supported by n
umerical studies.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberf
orce Road\, Cambridge
CONTACT:
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