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L4-08 · Causal discovery and its limits

Explain Markov equivalence, faithfulness, and the limits of discovering directions from observational data.

Level 4 icon Level 4 · Undergraduate
Objective. Explain Markov equivalence, faithfulness, and the limits of discovering directions from observational data.
Before this lesson. L4-02, L4-07, L3-09
Hands-on lab. Confounding and intervention

Learn

Causal discovery uses data and assumptions to constrain possible graphs. Constraint-based methods test conditional independences. Score-based methods compare graph scores under a model class. Functional-model methods use additional restrictions on mechanisms and noise. Every approach needs assumptions beyond a correlation matrix.

Markov-equivalent DAGs imply the same conditional independences. Without extra information, conditional independence tests can identify an equivalence class rather than one unique DAG. A collider can distinguish graphs that share a skeleton, but many edge directions remain unresolved even when all tests are exact.

Faithfulness excludes independences produced by exact parameter cancellation rather than graph separation. Finite samples can also hide weak dependencies. Continuous optimization methods such as NOTEARS impose an acyclicity constraint, but a converged objective does not remove assumptions about functional form, hidden causes, measurement, or identifiability.

Practice

Solution

The collider graph A→B←C blocks the only A-to-C path without conditioning, so it implies marginal independence. The directed chain leaves that path open and does not imply marginal independence.

Check your understanding

What does a DAG optimization solver returning one graph establish by itself?

Show the answer

C. That it returned a solution under its model and objective

An optimization result is conditional on its objective and assumptions. It does not itself prove causal sufficiency or a unique physical explanation.

Sources

This lesson draws on Spirtes et al., n.d.Peters et al., 2017Zheng et al., 2018.

Next: L4-09 · Counterfactual reasoning

References
  1. Spirtes, Glymour, & Scheines. (n.d.). Causation, Prediction, and Search. https://www.cs.cmu.edu/afs/cs.cmu.edu/project/learn-43/lib/photoz/.g/web/.g/scottd/fullbook.pdf
  2. Peters, J., Janzing, D., & Scholkopf, B. (2017). Elements of Causal Inference. https://mitpress.mit.edu/9780262037310/elements-of-causal-inference/
  3. Zheng, X., Aragam, B., Ravikumar, P., & Xing, E. P. (2018). DAGs with NO TEARS: Continuous Optimization for Structure Learning. https://arxiv.org/abs/1803.01422
  4. Bareinboim, E. (2025). Causal Artificial Intelligence: A Roadmap for Building Causally Intelligent Systems. https://causalai-book.net/