Papers › Minimax Optimal Algorithms with Fixed-k-Nearest Neighbors

Minimax Optimal Algorithms with Fixed-k-Nearest Neighbors

5 Feb 2022arXiv:2202.02464archive 2025-07-28

J. Jon Ryu, Young-Han Kim

This paper presents how to perform minimax optimal classification, regression, and density estimation based on fixed-k nearest neighbor (NN) searches. We consider a distributed learning scenario, in which a massive dataset is split into smaller groups, where the k-NNs are found for a query point with respect to each subset of data. We propose \emph{optimal} rules to aggregate the fixed-k-NN information for classification, regression, and density estimation that achieve minimax optimal rates for the respective problems. We show that the distributed algorithm with a fixed k over a sufficiently large number of groups attains a minimax optimal error rate up to a multiplicative logarithmic factor under some regularity conditions. Roughly speaking, distributed k-NN rules with M groups has a performance comparable to the standard Θ(kM)-NN rules even for fixed k.

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