# A New Distribution on the Simplex with Auto-Encoding Applications

arXiv: https://arxiv.org/abs/1905.12052 · HTML: https://mlsanity.com/paper/1905.12052/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2019.

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

- [Bayesian Nonparametrics for Offline Skill Discovery](https://mlsanity.com/paper/2202.04675/) (2022)
- [Stabilizing the Kumaraswamy Distribution](https://mlsanity.com/paper/2410.00660/) (2024)
- [The VampPrior Mixture Model](https://mlsanity.com/paper/2402.04412/) (2024)

## Abstract (arXiv)

We construct a new distribution for the simplex using the Kumaraswamy distribution and an ordered stick-breaking process. We explore and develop the theoretical properties of this new distribution and prove that it exhibits symmetry under the same conditions as the well-known Dirichlet. Like the Dirichlet, the new distribution is adept at capturing sparsity but, unlike the Dirichlet, has an exact and closed form reparameterization--making it well suited for deep variational Bayesian modeling. We demonstrate the distribution's utility in a variety of semi-supervised auto-encoding tasks. In all cases, the resulting models achieve competitive performance commensurate with their simplicity, use of explicit probability models, and abstinence from adversarial training.