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Thursday, May 17
Machine Learning
Model Selection in High-Dimensions with Complexities
Thu, May 17, 1:30 PM - 3:00 PM
Regency Ballroom A
 

Expected Volume Confidence Region Complexity (EVCR_COMP) Criterion in High Dimensions with Applications (304382)

*Hamparsum Bozdogan, University of Tennessee 

Keywords: Volume, Expected Volume, Confidence Regions, High Dimensional Multivariate Models, and Complexity.

In this paper we introduce and develop a new Expected Volume Confidence Region Complexity (EVCR_COMP) Criterion in High Dimensions. Derivation and computation of EVCR_COMP is carried out explicitly in multivariate modeling of high dimensions. Expected volume is analogous to distances under different covariance structures. For a given p, dimension of the data, significance level a, and the sample size n, minus twice the log of EVCR combined with the lack-of-fit of a model produces a new model selection criterion called EVCR_COMP, analogous to Akaike’s information criterion (AIC), Schwarz’s Bayesian criterion (SBC or BIC), and the information complexity (ICOMP) criterion of Bozdogan to choose the best fitting model among the competing alternative models. We show numerical examples on real and as well as simulated data sets in choosing the number of factors in factor analytic (FA) model and the probabilistic principal component analysis (PPCA) model in choosing the number of PPCs.