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

TL;DR

discretize_distributions is a Python package that efficiently approximates Gaussian mixture distributions with guarantees on Wasserstein distance, enabling scalable and accurate quantization for control and verification tasks.

Contribution

The paper introduces a new Python package that combines state-of-the-art quantization methods with scalability and modularity for Gaussian mixture approximation.

Findings

Accurately approximates high-dimensional Gaussian mixtures

Provides low computational cost for large-scale problems

Guarantees approximation error in Wasserstein distance

Abstract

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.