Lower bounds for Bayes error estimation

András Antos, Luc Devroye, László Györfi

Research output: Contribution to journalArticle

36 Citations (Scopus)


We give a short proof of the following result. Let (X, Y) be any distribution on N×{0, 1}, and let (X1, Y1), ..., (Xn, Yn) be an i.i.d. sample drawn from this distribution. In discrimination, the Bayes error L* = infg P{g(X)≠Y} is of crucial importance. Here we show that without further conditions on the distribution of (X, Y), no rate-of-convergence results can be obtained. Let φn(X1, Y1, ..., Xn, Yn) be an estimate of the Bayes error, and let {φn(.)} be a sequence of such estimates. For any sequence {an} of positive numbers converging to zero, a distribution of (X, Y) may be found such that E{|L*-φn(X1, Y1, ..., Xn, Yn)|}≥an infinitely often.

Original languageEnglish
Pages (from-to)643-645
Number of pages3
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number7
Publication statusPublished - Jan 1 1999


ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics

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