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Activity Number: 369
Type: Contributed
Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Learning and Data Mining
Abstract #315884 View Presentation
Title: Model Selection in High-Dimensional Misspecified Models
Author(s): Pallavi Basu*
Companies: University of Southern California
Keywords: Model Misspecification ; High-dimensionality ; Model Selection ; Variable Selection ; AIC, BIC ; KL divergence
Abstract:

Model selection is indispensable to high-dimensional sparse modeling in selecting the best set of covariates among a sequence of candidate models. Most existing work assumes implicitly that the model is correctly specified or of fixed dimensions. Yet model misspecification and high dimensionality are common in real applications. In this paper, we investigate two classical Kullback-Leibler divergence and Bayesian principles of model selection in the setting of high-dimensional misspecified models. Asymptotic expansions of these principles reveal that the effect of model misspecification is crucial and should be taken into account, leading to the generalized AIC and generalized BIC in high dimensions. With a natural choice of prior probabilities, 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 covariance contrast matrix estimator in a general setting. Our results and new method are supported by numerical studies.

Joint work with Yang Feng and Jinchi Lv.


Authors who are presenting talks have a * after their name.

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