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.

翻译：我们研究分布计算图的一般框架：这类计算图的输入是概率分布而非点值。我们分析了当使用连续概率分布的有限近似来评估这些计算图时产生的离散化误差。这种近似可能源于使用离散表示来表示连续实值分布，或从样本构建经验分布（也可能是另一个分布计算图的输出）。我们在Wasserstein-1距离的意义上建立了非渐近误差界，且无需对计算图施加结构假设。