Decomposing Epistemic Uncertainty for Causal Decision Making

Causal inference from observational data provides strong evidence for the best action in decision-making without performing expensive randomized trials. The effect of an action is usually not identifiable under unobserved confounding, even with an infinite amount of data. Recent work uses neural networks to obtain practical bounds to such causal effects, which is often an intractable problem. However, these approaches may overfit to the dataset and be overconfident in their causal effect estimates. Moreover, there is currently no systematic approach to disentangle how much of the width of causal effect bounds is due to fundamental non-identifiability versus how much is due to finite-sample limitations. We propose a novel framework to address this problem by considering a confidence set around the empirical observational distribution and obtaining the intersection of causal effect bounds for all distributions in this confidence set. This allows us to distinguish the part of the interval that can be reduced by collecting more samples, which we call sample uncertainty, from the part that can only be reduced by observing more variables, such as latent confounders or instrumental variables, but not with more data, which we call nonID uncertainty. The upper and lower bounds to this intersection are obtained by solving min-max and max-min problems with neural causal models by searching over all distributions that the dataset might have been sampled from, and all SCMs that entail the corresponding distribution. We demonstrate via extensive experiments on synthetic and real-world datasets that our algorithm can determine when collecting more samples will not help determine the best action. This can guide practitioners to collect more variables or lean towards a randomized study for best action identification.