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Minimax Optimal Estimation of KL Divergence for Continuous Distributions

Information Theory 2020-02-27 v1 math.IT Machine Learning

Abstract

Estimating Kullback-Leibler divergence from identical and independently distributed samples is an important problem in various domains. One simple and effective estimator is based on the k nearest neighbor distances between these samples. In this paper, we analyze the convergence rates of the bias and variance of this estimator. Furthermore, we derive a lower bound of the minimax mean square error and show that kNN method is asymptotically rate optimal.

Keywords

Cite

@article{arxiv.2002.11599,
  title  = {Minimax Optimal Estimation of KL Divergence for Continuous Distributions},
  author = {Puning Zhao and Lifeng Lai},
  journal= {arXiv preprint arXiv:2002.11599},
  year   = {2020}
}
R2 v1 2026-06-23T13:54:49.325Z