Fast and Bayes-consistent nearest neighbors

Research output: Contribution to journalConference articlepeer-review

1 Scopus citations


Research on nearest-neighbor methods tends to focus somewhat dichotomously either on the statistical or the computational aspects - either on, say, Bayes consistency and rates of convergence or on techniques for speeding up the proximity search. This paper aims at bridging these realms: to reap the advantages of fast evaluation time while maintaining Bayes consistency, and further without sacrificing too much in the risk decay rate. We combine the locality-sensitive hashing (LSH) technique with a novel missing-mass argument to obtain a fast and Bayes-consistent classifier. Our algorithm's prediction runtime compares favorably against state of the art approximate NN methods, while maintaining Bayes-consistency and attaining rates comparable to minimax. On samples of size n in Rd, our pre-processing phase has runtime O(dn log n), while the evaluation phase has runtime O(d log n) per query point.

Original languageEnglish
Pages (from-to)1276-1286
Number of pages11
JournalProceedings of Machine Learning Research
StatePublished - 1 Jan 2020
Event23rd International Conference on Artificial Intelligence and Statistics, AISTATS 2020 - Virtual, Online
Duration: 26 Aug 202028 Aug 2020

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


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