consistent density functional estimators using k nearest neighbors
Name: Shouvik Ganguly
Grad Year: 2020
Jongha Ryu, email@example.com
Given i.i.d. samples drawn from an unknown density, how can one estimate a functional of the density? In this work, a unified approach which can be applied to various functionals including Shannon entropy and Renyi entropy is proposed using k-nearest-neighbor distances from the i.i.d. samples. In contrast to the existing estimators, the proposed estimator is constructed so as to be asymptotically unbiased. The finite-sample analysis of the estimator under mild regularity conditions is performed to show mean-squared consistency of our estimator, and the theoretical guarantees are supported by experiments on certain well-known distributions. This approach can also be naturally generalized to estimating f-divergences.
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