Distributionally robust PCA using data-adaptive Wasserstein geometry yields consistent subspace estimators with a tractable surrogate objective and data-driven radius of order n^{-1/2}.
arXiv preprint arXiv:2503.02494 , year=
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A smoothing-aware AdaGrad Riemannian gradient method achieves O(ε^{p-4}) global complexity for non-Lipschitz manifold optimization with p-norm penalties (p in (0,1]), recovering the known O(ε^{-3}) rate when p=1.
Develops an inexact proximal linearization algorithm for composite optimization on manifolds achieving O(ε^{-3}) oracle complexity and convergence to stationary points under KL property assumptions.
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Distributionally Robust PCA with Data-Adaptive Wasserstein Geometry
Distributionally robust PCA using data-adaptive Wasserstein geometry yields consistent subspace estimators with a tractable surrogate objective and data-driven radius of order n^{-1/2}.
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