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arXiv · 1411.4342

Influence Functions for Machine Learning: Nonparametric Estimators for Entropies, Divergences and Mutual Informations

Kirthevasan Kandasamy·Akshay Krishnamurthy·Barnabas Poczos·Larry Wasserman·James M. Robins
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Abstract

We propose and analyze estimators for statistical functionals of one or more distributions under nonparametric assumptions. Our estimators are based on the theory of influence functions, which appear in the semiparametric statistics literature. We show that estimators based either on data-splitting or a leave-one-out technique enjoy fast rates of convergence and other favorable theoretical properties. We apply this framework to derive estimators for several popular information theoretic quantities, and via empirical evaluation, show the advantage of this approach over existing estimators.

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Kirthevasan Kandasamy, Akshay Krishnamurthy, Barnabas Poczos, Larry Wasserman, James M. Robins. 2014-11-17. Influence Functions for Machine Learning: Nonparametric Estimators for Entropies, Divergences and Mutual Informations. https://arxiv.org/abs/1411.4342

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