For regression of 1-Lipschitz functions under log-concave measures with Gaussian-like polynomial approximation, low-degree polynomial estimators achieve the minimax L2 risk of order log d / log n when n is subexponential in d.
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Entropy and Learning of Lipschitz Functions under Log-Concave Measures
For regression of 1-Lipschitz functions under log-concave measures with Gaussian-like polynomial approximation, low-degree polynomial estimators achieve the minimax L2 risk of order log d / log n when n is subexponential in d.