Results on Counterfactual Invariance
This work addresses foundational questions in causal inference for researchers, but it is incremental as it builds on existing definitions without introducing new methods.
The paper analyzes counterfactual invariance theoretically, showing that it implies conditional independence but not vice versa, and that in discrete causal models, counterfactually invariant functions are often constrained to specific variables or constants.
In this paper we provide a theoretical analysis of counterfactual invariance. We present a variety of existing definitions, study how they relate to each other and what their graphical implications are. We then turn to the current major question surrounding counterfactual invariance, how does it relate to conditional independence? We show that whilst counterfactual invariance implies conditional independence, conditional independence does not give any implications about the degree or likelihood of satisfying counterfactual invariance. Furthermore, we show that for discrete causal models counterfactually invariant functions are often constrained to be functions of particular variables, or even constant.