A theoretical investigation of several model selection criteria for dimensionality reduction

摘要: Based on the problem of determining hidden dimensionality (or number latent factors) Factor Analysis (FA) model, this paper provides a theoretic comparison several classical model selection criteria, including Akaike's Information Criterion (AIC), Bozdogan's Consistent (CAIC), Hannan-Quinn information criterion (HQC), Schwarz's Bayesian (BIC). We focus building up partial order relative underestimation tendency. The is shown to be AIC, HQC, BIC, and CAIC, indicating probabilities from small large. This indicates an performances great extent, because underestimations usually take major proportion wrong selections when sample size population signal-to-noise ratio (SNR, defined as smallest variance dimensions noise) decrease. Synthetic experiments by varying values SNR training N verify theoretical results.