高效量化高斯混合分布，保证误差上限，适合控制系统验证。
discretize_distributions: Efficient Quantization of Gaussian Mixtures with Guarantees in Wasserstein Distance
- 基于最优传输距离设计离散化方法，支持高维大模型
- 在高维、退化场景下仍保持低计算成本与高精度
- 模块化接口可嵌入控制与验证系统，支持自定义策略
我们提出 discretize_distributions，一个用于高效构建高斯混合分布离散近似并提供瓦瑟斯坦距离误差保证的 Python 工具包。该工具包实现了高斯混合模型的前沿量化方法，并通过扩展提升可扩展性。它还集成了互补的 σ-点方法，提供模块化接口，支持自定义方案，并可集成到网络物理系统的控制与验证流程中。我们在多种场景下进行了基准测试，包括高维、大规模及退化高斯混合分布，结果表明该工具包能在极低计算开销下实现高精度近似。
原文摘要 · Abstract (English)
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.
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