A1754
Title: Generalized information criterion for rank selection in high-dimensional CCA
Authors: Jia-Rou Liu - National Taiwan University (Taiwan) [presenting]
Hung Hung - National Taiwan University (Taiwan)
Abstract: Determining the appropriate number of Canonical pairs (rank) in high-dimensional Canonical Correlation Analysis (CCA) remains challenging, particularly under model misspecification where conventional criteria such as AIC and BIC often perform poorly. A Generalized Information Criterion (GIC) for robust rank selection in CCA is proposed. An explicit closed-form expression for the GIC penalty is derived using the score and influence functions of the CCA parameters. Through the eigenvalue representation underlying CCA, the resulting penalty incorporates the magnitude of eigenvalues, in contrast to conventional criteria that depend solely on the number of parameters. The asymptotic properties of GIC are established and the gap conditions required for selection consistency are identified. Extensive simulations under varying signal strengths and noise structures, including both simple and Generalized spiked covariance models, support the theoretical findings. Compared with existing methods, GIC more effectively excludes noise eigenvalues than AIC while remaining more sensitive than BIC in detecting signal eigenvalues. Overall, the proposed method provides rigorous theoretical foundations and a practically robust approach for rank determination in high-dimensional CCA.
