How to find hidden patterns in high-dimensional data 100× faster?

Sufficient dimension reduction finds a low-dimensional subspace that captures everything about the response variable—but existing methods become prohibitively slow in high dimensions. This work recasts the problem on the Stiefel manifold (a geometric structure for orthogonal matrices) and uses Riemannian stochastic gradients with nearest-neighbor localization, yielding SMAVE. The method achieves the same statistical accuracy as competitors while running orders of magnitude faster on real datasets, with guaranteed convergence rates.