Distributional Computational Graphs: Error Bounds
This work addresses error analysis for computational graphs with distributional inputs, which is incremental as it builds on existing frameworks by providing theoretical bounds.
The paper tackles the problem of discretization error in distributional computational graphs, where inputs are probability distributions, by establishing non-asymptotic error bounds in terms of the Wasserstein-1 distance without structural assumptions on the graph.
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.