Towards Bounding Causal Effects under Markov Equivalence
Alexis Bellot
TL;DR
The paper addresses bounding causal effects when only observational data and a Partial Ancestral Graph (PAG) are available, i.e., under Markov equivalence rather than a fully specified diagram. It introduces a PAG-based partial identification framework (Partial IDP) that yields analytic lower and upper bounds on causal effects by exploiting invariances and a decomposition of $Q[\C]$ into $pc$-components and regions. It proves that these bounds can be tighter than Manski's natural bounds and provides algorithms to compute them, along with a discussion of their limitations and scalability. The work also investigates enumeration strategies over Loyal Equivalent Graphs (LEGs) and Maximally Bi-directed Diagrams (MBD), showing expressiveness equivalence with ME MAGs but highlighting substantial computational challenges for practical use in larger systems.
Abstract
Predicting the effect of unseen interventions is a fundamental research question across the data sciences. It is well established that in general such questions cannot be answered definitively from observational data. This realization has fuelled a growing literature introducing various identifying assumptions, for example in the form of a causal diagram among relevant variables. In practice, this paradigm is still too rigid for many practical applications as it is generally not possible to confidently delineate the true causal diagram. In this paper, we consider the derivation of bounds on causal effects given only observational data. We propose to take as input a less informative structure known as a Partial Ancestral Graph, which represents a Markov equivalence class of causal diagrams and is learnable from data. In this more ``data-driven'' setting, we provide a systematic algorithm to derive bounds on causal effects that exploit the invariant properties of the equivalence class, and that can be computed analytically. We demonstrate our method with synthetic and real data examples.