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Causal Discovery

causalrl learns causal structure from discrete observational data by constraint-based search, testing conditional independence with conditional mutual information. See Guarantees And Scope for the precise contract (faithfulness, the thresholded test).

PC — assuming no latent confounders

discover runs the PC algorithm and returns a CPDAG (a Markov-equivalence class of DAGs): unshielded colliders are oriented, then Meek's rules propagate. It assumes causal sufficiency (every common cause is observed) and faithfulness.

from causalrl import discover

cpdag = discover(data, ["X", "Y", "Z"])

discover_interventional refines the CPDAG toward the true DAG using experimental (L2) data via the invariance principle.

FCI — allowing latent confounders

When causal sufficiency cannot be assumed, discover_latent runs the FCI algorithm and returns a PAG (partial ancestral graph). FCI adds a Possible-D-SEP skeleton refinement (sound under latents) and the complete orientation rules R1–R10 (Zhang 2008, including selection bias). In a PAG:

  • a -> b — a is a cause of b;
  • a <-> b — a latent confounder of a and b (neither causes the other);
  • a circle endpoint o — undetermined by the equivalence class.
from causalrl import discover_latent

pag = discover_latent(data, ["X", "Y", "Z"])
print(pag.render())

Detecting a latent confounder

With C -> A, D -> B, and an unobserved L confounding A and B, the two unshielded colliders force arrowheads at both ends of A-B, so FCI reports the confounder as A <-> B:

pag = discover_latent(data, ["A", "B", "C", "D"])
assert pag.is_bidirected("A", "B")

M-bias — do not condition on the collider

The classic M-bias structure X <- L1 -> Z <- L2 -> Y (with L1, L2 latent) makes Z a collider. FCI marks arrowheads at Z (X o-> Z <-o Y) and finds no X-Y edge — a warning that conditioning on Z would open a spurious X-Y association.

Faithful to Spirtes, Glymour & Scheines (PC, FCI) and Zhang (2008) (the complete orientation rules).