Every LWF and AMP chain graph originates from a set of causal models
This work provides a theoretical foundation for chain graphs in causal inference, addressing a problem for researchers in statistics and machine learning, though it appears incremental as it builds on existing graph theory.
The paper tackled the justification of LWF and AMP chain graphs by proving that every chain graph is inclusion optimal with respect to the intersection of independence models from directed acyclic graphs under conditioning, showing these graphs can be accounted for by a set of causal models subject to selection bias.
This paper aims at justifying LWF and AMP chain graphs by showing that they do not represent arbitrary independence models. Specifically, we show that every chain graph is inclusion optimal wrt the intersection of the independence models represented by a set of directed and acyclic graphs under conditioning. This implies that the independence model represented by the chain graph can be accounted for by a set of causal models that are subject to selection bias, which in turn can be accounted for by a system that switches between different regimes or configurations.