Quantization of Probability Distributions via Divide-and-Conquer: Convergence and Error Propagation under Distributional Arithmetic Operations
Abstract
This article studies a general divide-and-conquer algorithm for approximating continuous one-dimensional probability distributions with finite mean. The article presents a numerical study that compares pre-existing approximation schemes with a special focus on the stability of the discrete approximations when they undergo arithmetic operations. The main results are a simple upper bound of the approximation error in terms of the Wasserstein-1 distance that is valid for all continuous distributions with finite mean. In many use-cases, the studied method achieve optimal rate of convergence, and numerical experiments show that the algorithm is more stable than pre-existing approximation schemes in the context of arithmetic operations.
Cite
@article{arxiv.2505.15283,
title = {Quantization of Probability Distributions via Divide-and-Conquer: Convergence and Error Propagation under Distributional Arithmetic Operations},
author = {Bilgesu Arif Bilgin and Olof Hallqvist Elias and Michael Selby and Phillip Stanley-Marbell},
journal= {arXiv preprint arXiv:2505.15283},
year = {2026}
}
Comments
Revised for publication. 36 pages, 20 figures. Comments welcome!