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The Nearest Neighbor Information Estimator is Adaptively Near Minimax Rate-Optimal
Jiantao Jiao · Weihao Gao · Yanjun Han

Wed Dec 05 02:00 PM -- 04:00 PM (PST) @ Room 210 #86
We analyze the Kozachenko–Leonenko (KL) fixed k-nearest neighbor estimator for the differential entropy. We obtain the first uniform upper bound on its performance for any fixed k over H\"{o}lder balls on a torus without assuming any conditions on how close the density could be from zero. Accompanying a recent minimax lower bound over the H\"{o}lder ball, we show that the KL estimator for any fixed k is achieving the minimax rates up to logarithmic factors without cognizance of the smoothness parameter s of the H\"{o}lder ball for $s \in (0,2]$ and arbitrary dimension d, rendering it the first estimator that provably satisfies this property.

Author Information

Jiantao Jiao (University of California, Berkeley)
Weihao Gao (UIUC)
Yanjun Han (Stanford University)

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