Theoretical Analysis and Comparison of Several Criteria on Linear Model Dimension Reduction

Authors:
Shikui Tu;Lei Xu
Affiliations:
Department of Computer Science and Engineering, The Chinese University of Hong Kong, Hong Kong, P.R. China;Department of Computer Science and Engineering, The Chinese University of Hong Kong, Hong Kong, P.R. China
Venue:
ICA '09 Proceedings of the 8th International Conference on Independent Component Analysis and Signal Separation
Year:
2009

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Abstract

Detecting the dimension of the latent subspace of a linear model, such as Factor Analysis, is a well-known model selection problem. The common approach is a two-phase implementation with the help of an information criterion. Aiming at a theoretical analysis and comparison of different criteria, we formulate a tool to obtain an order of their approximate underestimation-tendencies, i.e., AIC, BIC/MDL, CAIC, BYY-FA(a), from weak to strong under mild conditions, by studying a key statistic and a crucial but unknown indicator set. We also find that DNLL favors cases with slightly dispersed signal and noise eigenvalues. Simulations agree with the theoretical results, and also indicate the advantage of BYY-FA(b) in the cases of small sample size and large noise.