Causal effect bounds improved by using data symmetry constraints
Symmetry-Informed Causal Partial Identification
Machine Learning
Summary
Sometimes, figuring out cause and effect from data is tricky, and you can only estimate upper and lower bounds instead of exact numbers. This paper shows how known patterns in data, called symmetries, can help tighten those bounds and make estimates clearer. The authors introduce methods to include these symmetries as extra rules and prove this helps both in theory and practice. This means decisions based on uncertain data can be better informed by using this approach.
What this means in practice
- •For policy analysts: Estimate tighter causal effect bounds in policy decisions by incorporating known data patterns as constraints.
- •For biostatistics teams: Improve robustness of treatment effect estimates in medical studies using symmetry-informed constraints within partial identification frameworks.
Authors
Uzair Akbar, Zulfiqar Zaidi, Niki Kilbertus, Krikamol Muandet, Bo Dai
Abstract
Partial identification (PI) entails estimating bounds on causal effects by encoding different assumptions on data generation as a constrained optimization problem. Such bounds can suffice to inform policy decisions even if the causal effect itself is not identifiable. Often vacuous in practice, practitioners seek to exhaustively encode domain knowledge as additional constraints to make the PI bounds more informative. We introduce known data symmetries -- invariance of the causal effect under certain data transformations -- as a new source of constraints to inform PI. We operationalize this as a shape constraint on the causal function, and via a change of measure against which PI is posed using simple data pre-processing. Both approaches are shown to sharpen bounds under two canonical PI models. This is shown both theoretically for the population case, and via experiments in the finite-sample case. More broadly, our framework establishes data symmetries as a natural, underutilized source of background knowledge for robust causal inference.