3.2.1. pywhy_graphs.algorithms.pds

pywhy_graphs.algorithms.pds(graph: PAG, node_x: Union[int, float, str, Any], node_y: Optional[Union[int, float, str, Any]] = None, max_path_length: Optional[int] = None) → Set[Union[int, float, str, Any]]

Find all PDS sets between node_x and node_y.

Parameters:

graph : PAG

The graph.

node_x : node

The node ‘x’.

node_y : node

The node ‘y’.

max_path_length : optional, int

The maximum length of a path to search on. By default None, which sets it to 1000.

Returns:

dsep : set

The possibly d-separating set between node_x and node_y.

Notes

Possibly d-separating (PDS) sets are nodes V, along an adjacency paths from ‘node_x’ to some ‘V’, which has the following characteristics for every subpath triple <X, Y, Z> on the path:

• Y is a collider, or

• Y is a triangle (i.e. X, Y and Z form a complete subgraph)

If the path meets these characteristics, then ‘V’ is in the PDS set.

If Y is a triangle, then it will be uncertain with circular edges due to the fact that it is a shielded triple, not allowing us to infer that it is a collider. These are defined in [1] and [2].

References

[1]

Diego Colombo, Marloes H. Maathuis, Markus Kalisch, and Thomas S. Richardson. Learning high-dimensional directed acyclic graphs with latent and selection variables. The Annals of Statistics, 40(1):294 – 321, 2012. URL: https://doi.org/10.1214/11-AOS940, doi:10.1214/11-AOS940.

[2]

Peter Spirtes, Clark Glymour, and Richard Scheines. Causation, Prediction, and Search. Volume 81. The MIT Press, 01 1993. ISBN 978-1-4612-7650-0. doi:10.1007/978-1-4612-2748-9.