# Generalized Exponential Concentration Inequality for R'enyi Divergence Estimation

arXiv: https://arxiv.org/abs/1603.08589 · HTML: https://mlsanity.com/paper/1603.08589/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Mar 2016.

## Built on by (most cited first, 3 of 3)

- [Martingale Methods for Sequential Estimation of Convex Functionals and Divergences](https://mlsanity.com/paper/2103.09267/) (2021)
- [The Representation Jensen-Shannon Divergence](https://mlsanity.com/paper/2305.16446/) (2023)
- [Causal Feature Selection via Transfer Entropy](https://mlsanity.com/paper/2310.11059/) (2023)

## Abstract (arXiv)

Estimating divergences in a consistent way is of great importance in many machine learning tasks. Although this is a fundamental problem in nonparametric statistics, to the best of our knowledge there has been no finite sample exponential inequality convergence bound derived for any divergence estimators. The main contribution of our work is to provide such a bound for an estimator of R'enyi-α divergence for a smooth H"older class of densities on the d-dimensional unit cube [0, 1]d. We also illustrate our theoretical results with a numerical experiment.