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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Revisiting local regression: shape regularity, uniform rates, and the limits of random splits
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.