# Data Augementation with Polya Inverse Gamma

arXiv: https://arxiv.org/abs/1905.12141 · HTML: https://mlsanity.com/paper/1905.12141/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2019.

## Built on by (most cited first, 2 of 2)

- [Gradient-free variational learning with conditional mixture networks](https://mlsanity.com/paper/2408.16429/) (2024)
- [Learning Coupled Subspaces for Multi-Condition Spike Data](https://mlsanity.com/paper/2410.19153/) (2024)

## Abstract (arXiv)

We use the theory of normal variance-mean mixtures to derive a data augmentation scheme for models that include gamma functions. Our methodology applies to many situations in statistics and machine learning, including Multinomial-Dirichlet distributions, Negative binomial regression, Poisson-Gamma hierarchical models, Extreme value models, to name but a few. All of those models include a gamma function which does not admit a natural conjugate prior distribution providing a significant challenge to inference and prediction. To provide a data augmentation strategy, we construct and develop the theory of the class of P'olya Inverse Gamma distributions. This allows scalable EM and MCMC algorithms to be developed. We illustrate our methodology on a number of examples, including gamma shape inference, negative binomial regression and Dirichlet allocation. Finally, we conclude with directions for future research.