# Exponential Concentration of a Density Functional Estimator

arXiv: https://arxiv.org/abs/1603.08584 · HTML: https://mlsanity.com/paper/1603.08584/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Mar 2016.

## Built on by (most cited first, 4 of 4)

- [A Differential Entropy Estimator for Training Neural Networks](https://mlsanity.com/paper/2202.06618/) (2022)
- [On sample complexity of conditional independence testing with Von Mises estimator with application to causal discovery](https://mlsanity.com/paper/2310.13553/) (2023)
- [Causal Feature Selection via Transfer Entropy](https://mlsanity.com/paper/2310.11059/) (2023)
- [Sample Complexity of Nonparametric Closeness Testing for Continuous Distributions and Its Application to Causal Discovery with Hidden Confounding](https://mlsanity.com/paper/2503.07475/) (2025)

## Abstract (arXiv)

We analyze a plug-in estimator for a large class of integral functionals of one or more continuous probability densities. This class includes important families of entropy, divergence, mutual information, and their conditional versions. For densities on the d-dimensional unit cube [0,1]d that lie in a β-H"older smoothness class, we prove our estimator converges at the rate O left( n^-fracββ + d right). Furthermore, we prove the estimator is exponentially concentrated about its mean, whereas most previous related results have proven only expected error bounds on estimators.