Choosing an Algorithm

A curated guide to the algorithms most Tetrad users should start with.

Tetrad provides many structure-learning algorithms. This short list highlights the most recommended ones, with crisp summaries and links to full per-algorithm pages.

If you’re new to Tetrad, start here.

🔍 Choosing an Algorithm

Most users choose between:

  • DAG/CPDAG algorithms (assume no hidden confounders)

  • PAG algorithms (allow hidden confounders and selection bias)

A quick rule of thumb:

  • No hidden confounders → Use DAG/CPDAG methods
    (FGES, BOSS, PC, PC-Max)

  • Hidden confounders possible → Use PAG methods
    (FCI, GFCI, BOSS-FCI, FCIT)

🔍 DAG / CPDAG Methods (No Latent Confounders)

PC — Peter–Clark Algorithm
🔍 Constraint-based • 🎛️ α-controlled • Output: CPDAG
Removes edges using CI tests and orients them using collider and propagation rules. A classic method offering explicit statistical control via α.
→ Full page: PC

PC-Max
🔍 Constraint-based • 🎛️ α-controlled • Output: CPDAG
Variant of PC that selects separating sets with maximum p-value, improving orientation accuracy.
→ Full page: PC-Max

FGES — Fast Greedy Equivalence Search
📏 Score-based • ⚡ Highly scalable • Output: CPDAG
Greedy forward–backward search optimizing BIC. Very fast and scalable; a strong general-purpose default.
→ Full page: FGES

BOSS — Best Order Score Search
📏 Score-based • 🎯 Order-based • Output: CPDAG
Searches over variable orders and uses Grow–Shrink Trees to score efficiently; often produces sharper orientations than FGES.
→ Full page: BOSS

🌀 PAG Methods (Hidden Confounders Allowed)

FCI — Fast Causal Inference
🔍 Constraint-based • 🧩 Latent-capable • Output: PAG
Extends PC with additional pruning and orientation rules (R0–R10) to represent latent confounding and selection bias correctly. The canonical PAG discovery algorithm.
→ Full page: FCI

GFCI — Greedy Fast Causal Inference
🌀 Hybrid • 🧩 Latent-capable • Output: PAG
Uses FGES to obtain a CPDAG, then upgrades it to a PAG via FCI-style pruning/orientation. Parent design for newer hybrids.
→ Full page: GFCI

BOSS-FCI
🌀 Hybrid • 🧩 Latent-capable • Output: PAG
Replaces FGES with BOSS, producing a sharper starting point and improved pruning/orientation accuracy. Excellent general-purpose PAG learner.
→ Full page: BOSS-FCI

FCIT — FCI with Targeted Testing
🌀 Hybrid • 🧩 Latent-capable • 🎯 Targeted CI tests • Output: PAG
Uses score-guided selective testing to avoid low-value CI tests, improving stability and accuracy while guaranteeing a legal PAG. Often outperforms both FCI and GFCI.
→ Full page: FCIT

🔧 Other Useful Algorithm Classes

Several other methods specialize in:

  • Orientation only (FASK, LOFS, skew-based methods)

  • Non-Gaussian structure (LiNGAM, ICA-based models)

  • Time-series (PCMCI)

  • Markov blankets

  • Deterministic relations

These are powerful in the right contexts but are not typical starting points.

→ See full catalog: Full Algorithm List

🎛 Choosing CI Tests & Scores (Quick Guide)

  • Continuous (Gaussian-ish): Fisher Z, SEM-BIC

  • Discrete: G-test or Chi-square; BDeu/BIC

  • Mixed or nonlinear: KCI / RCIT (slower), basis-function methods (scalable)

  • Covariance-only datasets: Use methods accepting covariance matrices (e.g., BOSS, FGES)

⚠️ Common Pitfalls and Fixes

  • Graph too dense: lower α (PC/FCI) or increase penalty (FGES/BOSS)

  • Graph too sparse: raise α or decrease penalty

  • Odd orientations: try PC-Max, BOSS, or minimal prior knowledge

  • Slow runtime: limit depth; use RFCI or FCIT; increase threads