Distributional Computational Graphs: Error Bounds

2026-01-22

AI Summary

This work investigates the discretization error arising in computational graphs that operate on probability distributions when finite discrete approximations are employed. By constructing a general framework for distributional computational graphs and leveraging Wasserstein-1 distance together with probabilistic discretization theory, the study establishes, for the first time, a non-asymptotic upper bound on error propagation without imposing structural assumptions on the graph. The result holds for arbitrary distributional computational graphs, thereby providing rigorous theoretical guarantees for distribution propagation algorithms and elucidating the mechanism by which discretization errors accumulate across complex computational pipelines.

Technology Category

Machine Learning: Probabilistic Circuits and Graphical ModelsReasoning under Uncertainty: Graphical ModelsConstraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsSocial Networks and Social Media: Influence propagation, information diffusion, and the prediction on networksResponsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

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.

Problem

• distributional computational graphs
• discretization error
• Wasserstein-1 distance
• probability distributions
• error bounds

Innovation

• distributional computational graphs
• discretization error
• Wasserstein-1 distance
• non-asymptotic error bounds
• empirical distribution