Teleporter Theory: A General and Simple Approach for Modeling Cross-World Counterfactual Causality

Abstract: Leveraging the development of structural causal model (SCM), researchers can establish graphical models for exploring the causal mechanisms behind machine learning techniques. As the complexity of machine learning applications rises, single-world interventionism causal analysis encounters theoretical adaptation limitations. Accordingly, cross-world counterfactual approach extends our understanding of causality beyond observed data, enabling hypothetical reasoning about alternative scenarios. However, the joint involvement of cross-world variables, encompassing counterfactual variables and real-world variables, challenges the construction of the graphical model. Twin network is a subtle attempt, establishing a symbiotic relationship, to bridge the gap between graphical modeling and the introduction of counterfactuals albeit with room for improvement in generalization. In this regard, we demonstrate the theoretical breakdowns of twin networks in certain cross-world counterfactual scenarios. To this end, we propose a novel teleporter theory to establish a general and simple graphical representation of counterfactuals, which provides criteria for determining teleporter variables to connect multiple worlds. In theoretical application, we determine that introducing the proposed teleporter theory can directly obtain the conditional independence between counterfactual variables and real-world variables from the cross-world SCM without requiring complex algebraic derivations. Accordingly, we can further identify counterfactual causal effects through cross-world symbolic derivation. We demonstrate the generality of the teleporter theory to the practical application. Adhering to the proposed theory, we build a plug-and-play module, and the effectiveness of which are substantiated by experiments on benchmarks.