Minimax Optimal Estimation of KL Divergence for Continuous Distributions

• URL: http://arxiv.org/abs/2002.11599v1
• Date: Wed, 26 Feb 2020 16:37:37 GMT
• Title: Minimax Optimal Estimation of KL Divergence for Continuous Distributions
• Authors: Puning Zhao, Lifeng Lai
• Abstract summary: Esting 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 between these samples.
• Score: 56.29748742084386
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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