3.1.11. 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:

Gmixed-edge-graph

Mixed edge causal graph.

xset

First set of nodes in G.

yset

Second set of nodes in G.

zset

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

directed_edge_namestr

Name of the directed edge, default is directed.

bidirected_edge_namestr

Name of the bidirected edge, default is bidirected.

undirected_edge_namestr

Name of the undirected edge, default is undirected.

Returns:

bbool

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

See also

networkx.algorithms.d_separation.is_d_separator

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.

3.1.11.1. 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