On the Semi-Markov Equivalence of Causal Models
This work addresses a foundational gap in causal inference for researchers dealing with incomplete data, though it appears incremental as it builds on prior characterizations of equivalence classes.
The paper tackles the problem of characterizing structural variability within semi-Markov equivalence classes of causal models without causal sufficiency, proposing a systematic method to construct models that produce specific marginal statistical dependencies.
The variability of structure in a finite Markov equivalence class of causally sufficient models represented by directed acyclic graphs has been fully characterized. Without causal sufficiency, an infinite semi-Markov equivalence class of models has only been characterized by the fact that each model in the equivalence class entails the same marginal statistical dependencies. In this paper, we study the variability of structure of causal models within a semi-Markov equivalence class and propose a systematic approach to construct models entailing any specific marginal statistical dependencies.