Distributional Computational Graphs: Error Bounds

TL;DR

This paper introduces a framework for distributional computational graphs, analyzing the discretization error when evaluating distributions with finite approximations, providing non-asymptotic error bounds in Wasserstein-1 distance.

Contribution

It develops a general analysis of discretization errors in distributional graphs, deriving non-asymptotic bounds without structural assumptions.

Findings

Provides non-asymptotic error bounds in Wasserstein-1 distance

Applies to various approximation methods including discretization and sampling

No structural assumptions required on the computational graph

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.