A Hierarchy of Graphical Models for Counterfactual Inferences
Hongshuo Yang, Elias Bareinboim
Graphical models have been widely used as parsimonious encoders of assumptions of the underlying structural causal models and provide a basis from which causal inferences can be performed. Models that encode stronger constraints tend to have higher expressive power at the expense of lower empirical falsifiability. In this paper, we define two new collections of distributions which include counterfactual quantities that become experimentally accessible under the counterfactual randomization action. Correspondingly, we provide two new classes of graphical models for encoding empirically testable constraints in these distributions. We further present a sound and complete calculus, based on counterfactual calculus, which licenses inference in these two new models with rules that are also fall within the empirically falsifiable boundary. In addition, we formulate a hierarchy over several graphical models based on the constraints they encode and study the fundamental trade-off between the expressive power and empirical falsifiability of different models across the hierarchy.