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SUMMARY:Model Selection in High-Dimensional Misspecified Models - Yang Fen
 g\, Columbia University
DTSTART:20141205T160000Z
DTEND:20141205T170000Z
UID:TALK54678@talks.cam.ac.uk
CONTACT:20082
DESCRIPTION:Model selection is indispensable to high-dimensional sparse mo
 deling in selecting the best set of covariates among a sequence of candida
 te models. Most existing work assumes implicitly that the model is correct
 ly specified or of fixed dimensions. Yet model misspecification and high d
 imensionality are common in real applications. In this paper\, we investig
 ate two classical Kullback-Leibler divergence and Bayesian principles of m
 odel selection in the setting of high-dimensional misspecified models. Asy
 mptotic expansions of these principles reveal that the effect of model mis
 specification is crucial and should be taken into account\, leading to the
  generalized AIC and generalized BIC in high dimensions. With a natural ch
 oice of prior probabilities\, we suggest the generalized BIC with prior pr
 obability which involves a logarithmic factor of the dimensionality in pen
 alizing model complexity. We further establish the consistency of the cova
 riance contrast matrix estimator in a general setting. Our results and new
  method are supported by numerical studies.
LOCATION:MR12\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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