Search Algorithms — By Type

This page lists all algorithms whose wrappers implement
edu.cmu.tetrad.algcomparison.algorithm.Algorithm in Tetrad 7.6.9.

Descriptions are based on the corresponding classes in
edu.cmu.tetrad.search.

This catalog provides a comprehensive overview of all structure-learning algorithms available in Tetrad, with links to full per-algorithm documentation.

If you are new to Tetrad or want a curated subset of recommended methods, start with
👉 Search Algorithms — Short List

Note: Many per-algorithm pages are still being added as part of an ongoing documentation update.

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Legend — Algorithm Categories

Badge	Category	Description
🔍	Constraint-based	Uses conditional independence (CI) tests
📏	Score-based	Optimizes a score such as BIC, BDeu, GIC
🌀	Hybrid	Combines score-based and CI-test stages

Extra Structural Badges

Badge	Meaning	Description
🧩	Latent-capable	Can output PAGs; handles latent confounding and selection bias
🔁	Time-series / lagged	Supports lagged variables (PCMCI, time-lag FGES/PC)
🎨	Non-Gaussian / ICA	Uses ICA, skewness, or higher-order moments
🧠	Multi-dataset	For multi-sample or cross-subject analyses
📦	Resampling / stability	Ensemble, bootstrap, or stability methods
🧪	Experimental	Research / nonstandard algorithms
🔧	Orientation-only	Orient edges from a fixed skeleton

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🔍 Constraint-Based Algorithms (CPDAG / PAG)

Use conditional independence tests to prune adjacencies and orient edges.

Algorithm	Description
Pc — PC 🔍	Classic constraint-based CPDAG search (CI-test–driven).
Pc-Max — PC-Max 🔍	PC variant maximizing p-value for collider orientation.
CPC — CPC 🔍	Conservative collider rule reducing false orientations.
Pcd — PCD ♻️	PC variant robust to deterministic relations.
PcMb PC-MB 🔍	Local Markov blanket discovery via PC-style logic.
Fas — FAS 🔍	Fast Adjacency Search (the adjacency phase of PC).
Fci — FCI 🔍🧩	Full PAG search with latent confounding & selection bias.
Rfci — RFCI 🔍🧩	Fast approximation to FCI (reduced complexity).
FciIod — FCI-IOD 🔍🧩🧠	FCI variant for multi-dataset / partially overlapping variable sets.
Pcmci — PCMCI 🔍🔁	CI-based causal discovery for time-series data.
Ccd — CCD 🔍	Cyclic Causal Discovery (allows feedback loops).

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📏 Score-Based Algorithms (CPDAG)

Optimize a score (BIC, GIC, BDeu, IS-BIC, etc.) over DAGs or equivalence classes.

Algorithm	Description
Fges — FGES 📏	Fast greedy equivalence search; highly scalable.
FgesMb — FGES-MB 📏	FGES variant specialized for Markov blankets.
Boss — BOSS 📏	Best Order Score Search over variable orderings.
RestrictedBoss — Restricted BOSS 📏	BOSS with parent/tier restrictions for speed.
Grasp — GRaSP 📏	Greedy Relaxations of Sparsest Permutation.
LV-Heuristic — LV-Heuristic 🪶	Heuristic PAG from BOSS DAG; lightweight alternative to FCI/FCIT.
Sp — SP 📏	Sparsest Permutation; exact but only for very small models.
Images 🧩🧠📏 — IMaGES	Multi-sample FGES with cross-sample consistency.
IMaGESBoss 🧩🧠📏 — IMaGES	Multi-sample BOSS with cross-sample consistency.

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🌀 Hybrid Algorithms (Score + FCI)

Start with a CPDAG from a score-based method, then apply FCI-style pruning/orientation to obtain a PAG.

Algorithm	Description
Gfci — GFCI 🌀🧩	FGES → FCI refinement yielding a PAG.
GraspFci — GRaSP-FCI 🌀🧩	GRaSP → FCI refinement.
BossFci — BOSS-FCI 🌀🧩	BOSS → FCI refinement.
SpFci — SP-FCI 🌀🧩	Sparsest Permutation → FCI refinement.
Fcit — FCIT 🌀🧩	Score-guided selective testing; efficient, legal-PAG output.

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🎨 Non-Gaussian, Moment-Based, and Orientation Algorithms

Use ICA, skewness, or higher-order moments to orient edges or to supplement a skeleton.

Algorithm	Description
DirectLingam — Direct LiNGAM 🎨	Direct LiNGAM for linear non-Gaussian models.
IcaLingam — ICA LiNGAM 🎨	ICA-based LiNGAM (classic).
IcaLingD — ICA LiNG-D 🎨	Cyclic LiNGAM (Lacerda et al.).
Fask — FASK 🎨	FAS skeleton + skewness-based orientation.
FaskVote — FASK-Vote 🎨📦	Voting ensemble of FASK.
Pairwise — Pairwise 🎨	Pairwise-skewness orientation.

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Nonlinear & Distribution-Shift Algorithms

Handle nonlinear functions, distribution shifts, or cyclic behavior.

Algorithm	Description
Cam — CAM	Causal Additive Model (nonlinear additive noise SEMs).
Dagma — DAGMA 📏	Continuous DAG optimization with smooth acyclicity constraint.
Cdnod — CD-NOD	Causal discovery under distributional changes.

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📦 Stability / Resampling / Ensemble Wrappers

Run algorithms repeatedly under resampling or varying penalties.

Algorithm	Description
StabilitySelection — Stability Selection 📦	Stability selection for edges across resampling.
StARS — StARS 📦	Stability Approach to Regularization Selection.
PagSamplingRfci — PAG Sampling RFCI 🔍🧩📦	RFCI on resampled/generated PAGs.
RfciBsc — RFCI-BSC 🔍🧩📦	RFCI with bootstrap/stability selection.

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🧪 Specialized / Utility Algorithms

Special-purpose, experimental, or workflow-specific methods.

Algorithm	Description
DM DM 🧪	Detect–Mimic (intermediate-latent preprocessing).
Cstar CStaR 🧪	Bounds on causal effects via edge-orientation patterns.
SingleGraphAlg Single Graph Alg 🧪	Wrapper for running Tetrad on a fixed imported graph.

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Latent Clustering (Measurement Block Discovery)

These algorithms discover measurement clusters—groups of indicators that behave as if they share a single latent parent.
See Latent Clusters for details.

Algorithm	Description
TSC	Trek Separation Clusters using rank constraints.
FOFC	First-Order Factor Clustering via pure tetrads.
FTFC	Fast Tetrad-Factor Clustering using sextads.
GFFC	Generalized Factor Finding Clustering (2×2 → 3×3 → …).
BPC	Build Pure Clusters (global purification & merging).

Once clusters are obtained, they can be treated as measurement blocks. These blocks may be supplied to algorithms that support:

• Blocks-Test-TS — a trek-separation conditional independence test over blocks;

• Blocks-BIC — a block-aware score.

In this mode, any algorithm that accepts a test and/or a score (PC, FGES, BOSS, GFCI, etc.) can be run on the latent layer: each cluster becomes a latent node, and Blocks-Test-TS / Blocks-BIC handle independence and scoring among the latent variables.

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Latent Structure / Measurement-Model Construction

Building on cluster discovery and block-based search, these algorithms explicitly construct latent variables or full measurement models before running structural search on the latent layer.

Algorithm	Description
Factor Analysis 🧩	Classical SEM-style factor analysis (measurement model).
Mimbuild Bollen 🧩	MIM builder using Bollen-style BlockSpec constraints.
Mimbuild PCA 🧩	PCA-based measurement model from pure clusters.