Non-causal connected

CPDAG

Rule table used for computing the parent adjustment distance for two CPDAGs according to the methods by Henckel et al. (2024b). For given sets $X$ and $Z$ , it finds certain nodes $y$ such that $Z$ cannot be used as an adjustment set with respect to $X$ and $y$ .

EDGES --> <--, ---
SETS X, W
COLORS init, poss-causal, non-causal
START ... [init] AT X
OUTPUT ... [non-causal]

... [init]        | ---, --> [poss-causal] | next not in X
... [init]        | <--      [non-causal]  | next not in X
--> [...]         | <--      [non-causal]  | next not in X and current in W
--- [poss-causal] | ---      [poss-causal] | next not in X and current not in W
... [poss-causal] | -->      [poss-causal] | next not in X and current not in W
--- [non-causal]  | ---      [non-causal]  | next not in X and current not in W
<-- [non-causal]  | ...      [non-causal]  | next not in X and current not in W
... [non-causal]  | -->      [non-causal]  | next not in X and current not in W

Graph type:

CPDAG

Applications:

Parent adjustment distance

References:

Henckel et al. (2024b)