Shape regularity of local sets is necessary and sufficient for optimal rates in local averaging estimators for Lipschitz regression functions, with k-NN succeeding by construction and random trees failing without geometric correction.
arXiv preprint arXiv:2110.15083 , year=
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SMAVE recasts MAVE for SDR as Riemannian optimization on the Stiefel manifold, yielding a stochastic algorithm with almost-sure convergence and improved runtime over OPG and RMAVE.
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Riemannian Stochastic Optimization for Sufficient Dimension Reduction
SMAVE recasts MAVE for SDR as Riemannian optimization on the Stiefel manifold, yielding a stochastic algorithm with almost-sure convergence and improved runtime over OPG and RMAVE.