Minimax Optimal Estimation of KL Divergence for Continuous Distributions.

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. [ABSTRACT FROM AUTHOR]