discretize_distributions: Efficient Quantization of Gaussian Mixtures with Guarantees in Wasserstein Distance
This work provides a practical tool for researchers and engineers working with cyber-physical systems, control, and verification who need efficient and reliable quantization of Gaussian mixtures.
The authors tackled the problem of approximating Gaussian mixture distributions with discrete approximations by developing a Python package that efficiently constructs such approximations with guaranteed error bounds in Wasserstein distance. They demonstrated that their package produces accurate approximations at low computational cost across various challenging examples.
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.