Exponential Concentration of a Density Functional Estimator

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Authors: Shashank Singh,Barnabás P óczos
Where published: NeurIPS 2014 12
ArXiv: 1603.08584
Document:  PDF  DOI 
Abstract URL: http://arxiv.org/abs/1603.08584v1

We analyze a plug-in estimator for a large class of integral functionals of one or more continuous probability densities. This class includes important families of entropy, divergence, mutual information, and their conditional versions. For densities on the $d$-dimensional unit cube $[0,1]^d$ that lie in a $\beta$-H\"older smoothness class, we prove our estimator converges at the rate $O \left( n^{-\frac{\beta}{\beta + d}} \right)$. Furthermore, we prove the estimator is exponentially concentrated about its mean, whereas most previous related results have proven only expected error bounds on estimators.

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