Influence Functions for Machine Learning: Nonparametric Estimators for Entropies, Divergences and Mutual Informations
This work provides improved estimators for information-theoretic quantities, which are incremental but useful for researchers in statistics and machine learning dealing with nonparametric data analysis.
The authors tackled the problem of estimating statistical functionals like entropies, divergences, and mutual informations under nonparametric assumptions, proposing estimators based on influence functions that achieve fast convergence rates and favorable theoretical properties. They demonstrated the advantage of this approach over existing estimators through empirical evaluation.
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.