pywhy_graphs.algorithms.inducing_path

pywhy_graphs.algorithms.inducing_path(G, node_x: Union[int, float, str, Any], node_y: Union[int, float, str, Any], L: Optional[Set] = None, S: Optional[Set] = None)

Checks if an inducing path exists between two nodes.

An inducing path is defined in [1].

Parameters:

G : Graph

The graph.

node_x : node

The source node.

node_y : node

The destination node.

L : Set

Nodes that are ignored on the path. Defaults to an empty set. See Notes for details.

S: Set

Nodes that are always conditioned on. Defaults to an empty set. See Notes for details.

Returns:

path : Tuple[bool, path]

A tuple containing a bool and a path if the bool is true, an empty list otherwise.

Notes

An inducing path intuitively is a path between two non-adjacent nodes that cannot be d-separated. Therefore, the path is always “active” regardless of what variables we condition on. L contains all the non-colliders, these nodes are ignored along the path. S contains nodes that are always conditioned on (hence if the ancestors of colliders are in S, then those collider paths are always “active”).

References

[1]

Jiji Zhang. On the completeness of orientation rules for causal discovery in the presence of latent confounders and selection bias. Artificial Intelligence, 172(16):1873–1896, 2008. URL: https://www.sciencedirect.com/science/article/pii/S0004370208001008, doi:https://doi.org/10.1016/j.artint.2008.08.001.