What Causal Discovery Can—and Cannot—Tell Us
Causal discovery is powerful because it turns conditional-independence patterns into constraints on possible causal structures. But the output is not the same thing as “the true causal graph.”
Start with data, end with a set of plausible causal structures
conditional independences
which directions are compatible?
Some edges and directions are learnable from the data structure
Which variables must be adjacent?
Some orientations can be identified from independence patterns.
Often several causal graphs remain observationally indistinguishable.
Useful conclusions
Rule out structures
Discovery algorithms can show that some causal configurations are incompatible with the observed independences under the assumed model class.
Expose ambiguity
A partially oriented graph is useful information: it tells you exactly which directions the data do not determine.
Important limits
Guarantee causal truth
The result depends on assumptions such as causal Markov, faithfulness, measurement quality, and the algorithm's treatment of latent confounding.
Resolve every direction
If multiple graphs imply the same observed independence structure, no purely observational algorithm can distinguish them without extra information.
Unmeasured variables change what is identifiable
If all common causes are measured
DAG-based algorithms can work within a simpler causal-sufficiency framework.
If hidden common causes may exist
Algorithms such as FCI return richer partial ancestral graphs that explicitly allow latent confounding and leave more endpoints unresolved when needed.
Same data, different assumptions, different causal conclusions
A graph learned under “no latent confounders” answers a different question from a graph learned while allowing hidden common causes. Similarly, temporal ordering, domain restrictions, or intervention knowledge can orient edges that observational data alone cannot.
Read partial graphs literally
Arrowhead
An arrowhead represents an orientation that is compelled under the algorithm's assumptions.
Circle endpoint
A circle is not “uncertainty to ignore.” It means the endpoint is not identified from the available information.
That distinction is one of the most important habits in reading causal-discovery output responsibly.
Causal discovery is a constraint-discovery tool, not a causal oracle
Its real value is in showing which causal statements are supported, which are ruled out, and which remain unresolved under a clearly stated set of assumptions.