Constraint and Score-Based Discovery
Routing Summary
Recovering causal structure (DAG / CPDAG / PAG) from observational data, from Glymour, Zhang & Spirtes (2019), “Review of Causal Discovery Methods Based on Graphical Models.”
- Need the big picture / which method to use? → Causal Discovery - Overview
- Need the assumptions linking d-separation to independence (Markov, faithfulness, CPDAG/MEC)? → Markov and Faithfulness Assumptions
- Need conditional-independence search (skeleton, v-structures, Meek rules; FCI/PAGs for confounders)? → PC Algorithm and Constraint-Based Discovery
- Need score-optimizing search (greedy forward/backward over equivalence classes, BIC)? → GES and Score-Based Discovery
- Need to orient direction beyond the equivalence class via noise asymmetry? → Functional Causal Models (LiNGAM, ANM)
Concept Map
| Note | Type | Role |
|---|---|---|
| Causal Discovery - Overview | overview | Goal of structure learning; three method families; Table 1 comparison; practical issues |
| Markov and Faithfulness Assumptions | definition | d-separation, local Markov, causal Markov + faithfulness, Markov equivalence class / CPDAG |
| PC Algorithm and Constraint-Based Discovery | concept | CI tests, skeleton, collider orientation, Meek rules; FCI, PAGs/MAGs for latent confounders |
| GES and Score-Based Discovery | concept | Greedy two-phase search over equivalence classes, BIC; GFCI hybrid |
| Functional Causal Models (LiNGAM, ANM) | concept | LiNGAM, ANM, PNL; identify direction via noise independence asymmetry |
Notes
- Causal Discovery - Overview — CONTAINS: definition of causal discovery / DGCMs; goal (recover DAG/CPDAG/PAG from observational data); the three families (constraint / score / FCM); Table 1 method comparison; practical challenges (time series, measurement error, selection bias, missing data).
- Markov and Faithfulness Assumptions — CONTAINS: paths/colliders/d-separation; local Markov condition; Causal Markov assumption; Causal Faithfulness assumption (no extra independencies); Markov Equivalence Class and CPDAG; equivalence invariants (skeleton + v-structures).
- PC Algorithm and Constraint-Based Discovery — CONTAINS: adjacency criterion; PC skeleton discovery (growing conditioning sets, separating sets); v-structure orientation rule; Meek orientation propagation; CPDAG output; FCI for latent confounders (PAG/MAG, bidirected edges, “o” marks); RFCI/GFCI.
- GES and Score-Based Discovery — CONTAINS: score functions (BIC); GES forward (FES) and backward (BES) phases; search over equivalence classes; convergence to same MEC as PC; weaker-than-faithfulness condition; GFCI hybrid for confounders.
- Functional Causal Models (LiNGAM, ANM) — CONTAINS: general FCM , noise-independence asymmetry test; LiNGAM (linear non-Gaussian, ICA/DirectLiNGAM, Darmois–Skitovich); ANM (nonlinear additive noise); PNL (post-nonlinear, most general); identifiability beyond the equivalence class; limitations.
Sources
- Glymour Zhang Spirtes 2019 - Review of Causal Discovery Methods.pdf — Glymour, Zhang & Spirtes (2019), Review of Causal Discovery Methods Based on Graphical Models, Frontiers in Genetics 10:524.