# Effective sample size approximations as entropy measures

arXiv: https://arxiv.org/abs/2602.22954 · HTML: https://mlsanity.com/paper/2602.22954/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 53 references that are in the map.
- First posted on arXiv 26 Feb 2026.

## Builds on (most cited first, 6 of 6)

- [Optimality in importance sampling: a gentle survey](https://mlsanity.com/paper/2502.07396/) (2025)
- [An exhaustive variable selection study for linear models of soundscape emotions: rankings and Gibbs analysis](https://mlsanity.com/paper/2207.12743/) (2022)
- [Spectral information criterion for automatic elbow detection](https://mlsanity.com/paper/2308.09108/) (2023)
- [Beware the Gini Index! A New Inequality Measure](https://mlsanity.com/paper/2110.01741/) (2021)
- [Universal and Automatic Elbow Detection for Learning the Effective Number of Components in Model Selection Problems](https://mlsanity.com/paper/2308.09102/) (2023)
- [An index of effective number of variables for uncertainty and reliability analysis in model selection problems](https://mlsanity.com/paper/2602.21403/) (2026)

## Built on by (most cited first, 1 of 1)

- [Nested Sampling: A Critical and Comprehensive Theoretical Guide](https://mlsanity.com/paper/2606.17916/) (2026)

## Abstract (arXiv)

In this work, we analyze alternative effective sample size (ESS) metrics for importance sampling algorithms, and discuss a possible extended range of applications. We show the relationship between the ESS expressions used in the literature and two entropy families, the R'enyi and Tsallis entropy. The R'enyi entropy is connected to the Huggins-Roy's ESS family introduced in citeHuggins15. We prove that that all the ESS functions included in the Huggins-Roy's family fulfill all the desirable theoretical conditions. We analyzed and remark the connections with several other fields, such as the Hill numbers introduced in ecology, the Gini inequality coefficient employed in economics, and the Gini impurity index used mainly in machine learning, to name a few. Finally, by numerical simulations, we study the performance of different ESS expressions contained in the previous ESS families in terms of approximation of the theoretical ESS definition, and show the application of ESS formulas in a variable selection problem.