CCA with infinitely many nonzero population canonical correlations

Investigate canonical correlation analysis in the regime where the number of nonzero population canonical correlations c_i is infinite (e.g., grows with the dimensions K and M), and determine the resulting asymptotic behavior of the sample canonical correlations and the associated sample canonical vectors, including whether outliers separate from the Wachter bulk and how the sample canonical vectors align with the population directions.

Background

In the high-dimensional “signal plus noise” setting, existing results characterize the case of finitely many nonzero canonical correlations (spikes). For distinct finite spikes, outlier locations and vector alignments are known, and distributional limits have been obtained.

The survey notes that extending this theory beyond finitely many spikes is not yet settled. Understanding models with an unbounded number of nonzero c_i would generalize the current finite-spike framework and clarify the spectral and vector-level behavior when signals proliferate.