Supplementary Material: Necessary and sufficient graphical conditions for optimal adjustment sets in causal graphical models with hidden variables [

There can be no loops or directed cycles. See Figure 1A for an example. The results also hold for Maximal Ancestral Graphs (MAG) [Richardson and Spirtes, 2002] without selection variables. Kinships are defined as usual: parents Our approach does not involve modified graph constructions as in van der Zander et al. [2019] and other works. A node is an ancestor and descendant of itself, but not a parent/child/spouse of itself.