# discretize_distributions: Efficient Quantization of Gaussian Mixtures with Guarantees in Wasserstein Distance

arXiv: https://arxiv.org/abs/2511.15854 · HTML: https://mlsanity.com/paper/2511.15854/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 19 references that are in the map.
- First posted on arXiv 19 Nov 2025.

## Builds on (most cited first, 4 of 4)

- [A Wasserstein-type distance in the space of Gaussian Mixture Models](https://mlsanity.com/paper/1907.05254/) (2019)
- [Finite Neural Networks as Mixtures of Gaussian Processes: From Provable Error Bounds to Prior Selection](https://mlsanity.com/paper/2407.18707/) (2024)
- [Efficient Uncertainty Propagation with Guarantees in Wasserstein Distance](https://mlsanity.com/paper/2506.08689/) (2025)
- [Formal Uncertainty Propagation for Stochastic Dynamical Systems with Additive Noise](https://mlsanity.com/paper/2505.11219/) (2025)

## Abstract (arXiv)

We present discretize_distributions, a Python package that efficiently constructs discrete approximations of Gaussian mixture distributions and provides guarantees on the approximation error in Wasserstein distance. The package implements state-of-the-art quantization methods for Gaussian mixture models and extends them to improve scalability. It further integrates complementary quantization strategies such as sigma-point methods and provides a modular interface that supports custom schemes and integration into control and verification pipelines for cyber-physical systems. We benchmark the package on various examples, including high-dimensional, large, and degenerate Gaussian mixtures, and demonstrate that discretize_distributions produces accurate approximations at low computational cost.