3.1.7. pywhy_graphs.networkx.m_separated

pywhy_graphs.networkx.m_separated(G, x, y, z, directed_edge_name='directed', bidirected_edge_name='bidirected', undirected_edge_name='undirected')

Check m-separation among ‘x’ and ‘y’ given ‘z’ in mixed-edge causal graph G, which may contain directed, bidirected, and undirected edges.

This implements the m-separation algorithm TESTSEP presented in [1] for ancestral mixed graphs. Further checks have ensure that it works for non-ancestral mixed graphs (e.g. ADMGs). The algorithm performs a breadth-first search over m-connecting paths between ‘x’ and ‘y’ (i.e. a path on which every node that is a collider is in ‘z’, and every node that is not a collider is not in ‘z’). The algorithm has runtime \(O(|E| + |V|)\) for number of edges \(|E|\) and number of vertices \(|V|\).

Parameters:

G : mixed-edge-graph

Mixed edge causal graph.

x : set

First set of nodes in G.

y : set

Second set of nodes in G.

z : set

Set of conditioning nodes in G. Can be empty set.

directed_edge_name : str

Name of the directed edge, default is directed.

bidirected_edge_name : str

Name of the bidirected edge, default is bidirected.

undirected_edge_name : str

Name of the undirected edge, default is undirected.

Returns:

b : bool

A boolean that is true if x is m-separated from y given z in G.

See also

networkx.algorithms.d_separation.d_separated

Notes

This wraps the networkx implementation, which only allows DAGs and does not have an ADMG representation.

References

[1]

B. van der Zander, M. Liśkiewicz, and J. Textor, “Separators and Adjustment Sets in Causal Graphs: Complete Criteria and an Algorithmic Framework,” Artificial Intelligence, vol. 270, pp. 1–40, May 2019, doi: 10.1016/j.artint.2018.12.006.

3.1.7.1. Examples using pywhy_graphs.networkx.m_separated

An introduction to causal graphs and how to use them

An introduction to causal graphs and how to use them