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Exponential Concentration of a Density Functional Estimator
Shashank Singh · Barnabas Poczos

Wed Dec 10 04:00 PM -- 08:59 PM (PST) @ Level 2, room 210D

We analyse 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-Holder smoothness class, we prove our estimator converges at the rate O(n^(1/(beta+d))). Furthermore, we prove that the estimator obeys an exponential concentration inequality about its mean, whereas most previous related results have bounded only expected error of estimators. Finally, we demonstrate our bounds to the case of conditional Renyi mutual information.

Author Information

Shashank Singh (Max Planck Institute for Intelligent Systems)
Barnabas Poczos (Carnegie Mellon University)

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