Discussion of “Independent component analysis by robust distance correlation”: toward a functional view of robust ICA

This discussion addresses PICARD, a robust approach to Independent Component Analysis (ICA) recently introduced by Leyder et al. My comments center on the distinction between two levels of robustness: that of the local dependence criterion — in particular the newly introduced bowl transform — and that of the full unmixing functional, the composite pipeline mapping the data distribution to the estimated sources. To clarify the mechanisms and trade-offs behind this robustness, I propose targeted empirical diagnostics, notably ablation studies and q- stability paths, where q is the scale parameter of the bowl transform. I further argue for a unified framework in which the dependence contrast, whitening functional, optimization scheme, and perturbation model are treated jointly.