Distributional Computational Graphs: Error Bounds
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Abstract (arXiv)
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.
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References · 5
- 2021Directed Acyclic Graph Neural Networkscited by 70
- 2024The Elements of Differentiable Programmingcited by 43
- 2022A Note on Monte Carlo Integration in High Dimensionscited by 5
- 2025Quantization of Probability Distributions via Divide-and-Conquer: Convergence and Error Propagation under Distributional Arithmetic Operationscited by 2
- 2025The Monte Carlo Method and New Device and Architectural Techniques for Accelerating Itcited by 1
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