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Causal faithfulness

As explained in Causal AI

A faithfulness violation is a case in which a conditional independence in the joint distribution does not correspond to a d-separation in the ground-truth causal graph.

A causal faithfulness violation occurs when variables are conditionally independent in the joint distribution even though the ground-truth causal DAG does not imply that independence through d-separation. Faithfulness reverses the causal Markov property: d-separation implies conditional independence under Markov, while faithfulness claims that observed conditional independence reflects d-separation. section 4.6.2 section 4.7

A distribution the DAG cannot represent

Consider a three-variable distribution that factorizes as P(x, y, z) = P(x, y)P(y, z)P(x, z). The resulting pairwise independence pattern can be detected in data, but no d-separation statement in a DAG represents it. This is a faithfulness violation: matching empirical independencies to graph constraints can exclude the true causal structure. section 4.6.2

Faithfulness matters when using conditional independencies to discover causal graphs:

  • Constraint-based algorithms, including PC, iteratively restrict candidate DAGs using empirical conditional-independence evidence and therefore rely on faithfulness. section 4.6.2
  • Violations mean that an independence detected in data may not identify a corresponding d-separation in the true graph, limiting discovery generalization. section 4.6.2
  • Treat discovery output as exploratory evidence rather than a replacement for constructing and defending a causal DAG, especially with latent variables. section 4.7

How Causal AI covers it

How deep it goes
Defines the converse of the Markov property, gives a factorization counterexample, and stops short of repairing discovery algorithms.
Examples
Uses a three-variable factorization whose observed independence pattern cannot be represented by DAG d-separation.
What it assumes
Assumes familiarity with DAGs, d-separation, conditional independence, and the causal Markov property.
What you can do after
Evaluate constraint-based causal-discovery results as heuristic evidence rather than definitive recovery of the ground-truth DAG.
How it connects
Connects causal Markov property, d-separation, conditional independence, causal discovery, latent variables, and Markov equivalence.
Cover of Causal AI
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Related concepts

This explainer was generated by Manning's knowledge graph from the text of Causal AI. The section links point to the parts of the book it draws on.