Quantization of Probability Distributions via Divide-and-Conquer: Convergence and Error Propagation under Distributional Arithmetic Operations
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911491026845696 |
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| author | Bilgin, Bilgesu Arif Elias, Olof Hallqvist Selby, Michael Stanley-Marbell, Phillip |
| author_facet | Bilgin, Bilgesu Arif Elias, Olof Hallqvist Selby, Michael Stanley-Marbell, Phillip |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15283 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantization of Probability Distributions via Divide-and-Conquer: Convergence and Error Propagation under Distributional Arithmetic Operations Bilgin, Bilgesu Arif Elias, Olof Hallqvist Selby, Michael Stanley-Marbell, Phillip Probability Computational Engineering, Finance, and Science Numerical Analysis 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. |
| title | Quantization of Probability Distributions via Divide-and-Conquer: Convergence and Error Propagation under Distributional Arithmetic Operations |
| topic | Probability Computational Engineering, Finance, and Science Numerical Analysis |
| url | https://arxiv.org/abs/2505.15283 |