# Quantization of Probability Distributions via Divide-and-Conquer: Convergence and Error Propagation under Distributional Arithmetic Operations

arXiv: https://arxiv.org/abs/2505.15283 · HTML: https://mlsanity.com/paper/2505.15283/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 May 2025.

## Built on by (most cited first, 2 of 2)

- [Distributional Computational Graphs: Error Bounds](https://mlsanity.com/paper/2601.16250/) (2026)
- [Dynamic Online Processor-Native Inference for State Estimation](https://mlsanity.com/paper/2607.12095/) (2026)

## Abstract (arXiv)

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.