High-dimensional theory for regularized CCA under misspecification

Establish rigorous high-dimensional asymptotics and robustness guarantees for regularized canonical correlation analysis (e.g., sparse or smooth CCA), especially when model assumptions are misspecified, including consistency and limit laws for canonical correlations and vectors under proportional growth of dimensions.

Background

Regularizations (sparsity, smoothness, etc.) are widely used to stabilize CCA and incorporate structure, often by penalized maximization formulations. While empirically successful, their theoretical properties in high-dimensional regimes are less understood, particularly under deviations from modeling assumptions.

The survey explicitly notes the lack of comprehensive theory for many such procedures in large dimensions and under misspecification.

References

We remark that from the theoretical perspective the behavior of many regularization procedures is not well-understood in the large-dimensional settings and/or in the situations when the assumptions are misspecified.

— Canonical Correlation Analysis: review (2411.15625 - Bykhovskaya et al., 23 Nov 2024) in Section “Subcritical signals and regularizations” (Chapter 4)