Distributional Computational Graphs: Error Bounds
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866912898455961600 |
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| author | Elias, Olof Hallqvist Selby, Michael Stanley-Marbell, Phillip |
| author_facet | Elias, Olof Hallqvist Selby, Michael Stanley-Marbell, Phillip |
| contents | We study a general framework of distributional computational graphs: computational graphs whose inputs are probability distributions rather than point values. We analyze the discretization error that arises when these graphs are evaluated using finite approximations of continuous probability distributions. Such an approximation might be the result of representing a continuous real-valued distribution using a discrete representation or from constructing an empirical distribution from samples (or might be the output of another distributional computational graph). We establish non-asymptotic error bounds in terms of the Wasserstein-1 distance, without imposing structural assumptions on the computational graph. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_16250 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Distributional Computational Graphs: Error Bounds Elias, Olof Hallqvist Selby, Michael Stanley-Marbell, Phillip Machine Learning Computational Engineering, Finance, and Science Numerical Analysis Probability Primary 60H10, 65C30, Secondary 60J60, 65C05 We study a general framework of distributional computational graphs: computational graphs whose inputs are probability distributions rather than point values. We analyze the discretization error that arises when these graphs are evaluated using finite approximations of continuous probability distributions. Such an approximation might be the result of representing a continuous real-valued distribution using a discrete representation or from constructing an empirical distribution from samples (or might be the output of another distributional computational graph). We establish non-asymptotic error bounds in terms of the Wasserstein-1 distance, without imposing structural assumptions on the computational graph. |
| title | Distributional Computational Graphs: Error Bounds |
| topic | Machine Learning Computational Engineering, Finance, and Science Numerical Analysis Probability Primary 60H10, 65C30, Secondary 60J60, 65C05 |
| url | https://arxiv.org/abs/2601.16250 |