Counterfactual Realizability
This work addresses a foundational problem in causal inference for researchers and practitioners, enabling more effective data collection in domains like fairness and reinforcement learning, though it builds incrementally on prior work by Bareinboim et al. (2015).
The paper tackles the problem of determining which counterfactual distributions can be directly sampled from in real-world environments, given physical constraints like time irreversibility, and resolves this by introducing a formal definition of realizability and a complete algorithm for such determinations. It shows that a counterfactual strategy provably dominates interventional and observational strategies in applications like causal fairness and causal reinforcement learning.
It is commonly believed that, in a real-world environment, samples can only be drawn from observational and interventional distributions, corresponding to Layers 1 and 2 of the Pearl Causal Hierarchy. Layer 3, representing counterfactual distributions, is believed to be inaccessible by definition. However, Bareinboim, Forney, and Pearl (2015) introduced a procedure that allows an agent to sample directly from a counterfactual distribution, leaving open the question of what other counterfactual quantities can be estimated directly via physical experimentation. We resolve this by introducing a formal definition of realizability, the ability to draw samples from a distribution, and then developing a complete algorithm to determine whether an arbitrary counterfactual distribution is realizable given fundamental physical constraints, such as the inability to go back in time and subject the same unit to a different experimental condition. We illustrate the implications of this new framework for counterfactual data collection using motivating examples from causal fairness and causal reinforcement learning. While the baseline approach in these motivating settings typically follows an interventional or observational strategy, we show that a counterfactual strategy provably dominates both.