# On the Normalizing Constant of the Continuous Categorical Distribution

arXiv: https://arxiv.org/abs/2204.13290 · HTML: https://mlsanity.com/paper/2204.13290/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 17 references that are in the map.
- First posted on arXiv 28 Apr 2022.

## Builds on (most cited first, 5 of 5)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [The continuous Bernoulli: fixing a pervasive error in variational autoencoders](https://mlsanity.com/paper/1907.06845/) (2019)
- [The continuous categorical: a novel simplex-valued exponential family](https://mlsanity.com/paper/2002.08563/) (2020)
- [Uses and Abuses of the Cross-Entropy Loss: Case Studies in Modern Deep Learning](https://mlsanity.com/paper/2011.05231/) (2020)

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

- [Data Augmentation for Compositional Data: Advancing Predictive Models of the Microbiome](https://mlsanity.com/paper/2205.09906/) (2022)

## Abstract (arXiv)

Probability distributions supported on the simplex enjoy a wide range of applications across statistics and machine learning. Recently, a novel family of such distributions has been discovered: the continuous categorical. This family enjoys remarkable mathematical simplicity; its density function resembles that of the Dirichlet distribution, but with a normalizing constant that can be written in closed form using elementary functions only. In spite of this mathematical simplicity, our understanding of the normalizing constant remains far from complete. In this work, we characterize the numerical behavior of the normalizing constant and we present theoretical and methodological advances that can, in turn, help to enable broader applications of the continuous categorical distribution. Our code is available at https://github.com/cunningham-lab/cb_and_cc/.