Papers › A New Distribution on the Simplex with Auto-Encoding Applications

A New Distribution on the Simplex with Auto-Encoding Applications

28 May 2019NeurIPS 2019 12arXiv:1905.12052archive 2025-07-28

Andrew Stirn, Tony Jebara, David A. Knowles

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.

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