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

arXiv: https://arxiv.org/abs/1411.4342 · HTML: https://mlsanity.com/paper/1411.4342/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2014.

## Built on by (most cited first, 5 of 5)

- [The Fundamental Limits of Structure-Agnostic Functional Estimation](https://mlsanity.com/paper/2305.04116/) (2023)
- [A Free Lunch with Influence Functions? Improving Neural Network Estimates with Concepts from Semiparametric Statistics](https://mlsanity.com/paper/2202.09096/) (2022)
- [Trying to Outrun Causality with Machine Learning: Limitations of Model Explainability Techniques for Identifying Predictive Variables](https://mlsanity.com/paper/2202.09875/) (2022)
- [Variational Weighting for Kernel Density Ratios](https://mlsanity.com/paper/2311.03001/) (2023)
- [Orthogonal Bootstrap: Efficient Simulation of Input Uncertainty](https://mlsanity.com/paper/2404.19145/) (2024)

## Abstract (arXiv)

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.