# Score matching for compositional distributions

arXiv: https://arxiv.org/abs/2012.12461 · HTML: https://mlsanity.com/paper/2012.12461/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Dec 2020.

## Built on by (most cited first, 5 of 5)

- [Robust and Scalable Bayesian Online Changepoint Detection](https://mlsanity.com/paper/2302.04759/) (2023)
- [Standardisation-function Kernel Stein Discrepancy: A Unifying View on Kernel Stein Discrepancy Tests for Goodness-of-fit](https://mlsanity.com/paper/2106.12105/) (2021)
- [Interaction Models and Generalized Score Matching for Compositional Data](https://mlsanity.com/paper/2109.04671/) (2021)
- [Should the Boundary Term Be Learned in Reflected Diffusion? Conormal Trace and Reflection Masking](https://mlsanity.com/paper/2608.03469/) (2026)
- [Robust Bayesian Inference for Unnormalized Models with Mixed-Domain Data](https://mlsanity.com/paper/2609.01783/) (2026)

## Abstract (arXiv)

Compositional data and multivariate count data with known totals are challenging to analyse due to the non-negativity and sum-to-one constraints on the sample space. It is often the case that many of the compositional components are highly right-skewed, with large numbers of zeros. A major limitation of currently available estimators for compositional models is that they either cannot handle many zeros in the data or are not computationally feasible in moderate to high dimensions. We derive a new set of novel score matching estimators applicable to distributions on a Riemannian manifold with boundary, of which the standard simplex is a special case. The score matching method is applied to estimate the parameters in a new flexible truncation model for compositional data and we show that the estimators are scalable and available in closed form. Through extensive simulation studies, the scoring methodology is demonstrated to work well for estimating the parameters in the new truncation model and also for the Dirichlet distribution. We apply the new model and estimators to real microbiome compositional data and show that the model provides a good fit to the data.