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 non-ID 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.

Approximate Causal Effect Identification under Weak Confounding

Causal effect estimation has been studied by many researchers when only observational data is available. Sound and complete algorithms have been developed for pointwise estimation of identifiable causal queries. For non-identifiable causal queries, researchers developed polynomial programs to estimate tight bounds on causal effect. However, these are computationally difficult to optimize for variables with large support sizes. In this paper, we analyze the effect of "weak confounding" on causal estimands. More specifically, under the assumption that the unobserved confounders that render a query non-identifiable have small entropy, we propose an efficient linear program to derive the upper and lower bounds of the causal effect. We show that our bounds are consistent in the sense that as the entropy of unobserved confounders goes to zero, the gap between the upper and lower bound vanishes. Finally, we conduct synthetic and real data simulations to compare our bounds with the bounds obtained by the existing work that cannot incorporate such entropy constraints and show that our bounds are tighter for the setting with weak confounders.