Towards Bounding Causal Effects under Markov Equivalence

TL;DR

This paper introduces a method to derive bounds on causal effects using Partial Ancestral Graphs, which represent Markov equivalence classes, enabling data-driven causal inference without fully identifying the causal diagram.

Contribution

It presents a systematic algorithm to compute bounds on causal effects from observational data using Partial Ancestral Graphs, relaxing the need for a fully specified causal diagram.

Findings

The method can be applied to synthetic data to accurately estimate bounds.

The approach is demonstrated on real data examples, showing practical utility.

Bounds derived are consistent with known causal effects in tested scenarios.

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.