A Concentration Result of Estimating Phi-Divergence using Data Dependent Partition

01/02/2018

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by   Fengqiao Luo, et al.

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Estimation of the ϕ-divergence between two unknown probability distributions using empirical data is a fundamental problem in information theory and statistical learning. We consider a multi-variate generalization of the data dependent partitioning method for estimating divergence between the two unknown distributions. Under the assumption that the distribution satisfies a power law of decay, we provide a convergence rate result for this method on the number of samples and hyper-rectangles required to ensure the estimation error is bounded by a given level with a given probability.