Influence Functions for Machine Learning: Nonparametric Estimators for Entropies, Divergences and Mutual Informations
Machine Learning
2015-07-21 v3 Artificial Intelligence
Machine Learning
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.
Cite
@article{arxiv.1411.4342,
title = {Influence Functions for Machine Learning: Nonparametric Estimators for Entropies, Divergences and Mutual Informations},
author = {Kirthevasan Kandasamy and Akshay Krishnamurthy and Barnabas Poczos and Larry Wasserman and James M. Robins},
journal= {arXiv preprint arXiv:1411.4342},
year = {2015}
}