Methods

Andrey has 49 supported methods and 1 experimental method.

Start from your data

Data	Method	Graph	Families
Continuous Numbers on a scale, one column per variable	PC andrey.pc	CPDAG	Constraint-based 9 Score-based 13 Permutation-based 6 Functional causal models 7 Temporal causal discovery 8 Latent variables 4 Pairwise direction 3
Categorical Labels, such as yes and no, coded as whole numbers	PC andrey.pc	CPDAG	Constraint-based 8 Score-based 8 Permutation-based 6 Temporal causal discovery 3
Mixed Some columns numbers, some labels	PC andrey.pc	CPDAG	Constraint-based 8 Score-based 8 Permutation-based 6 Temporal causal discovery 3
Missing values Some cells are empty	PC andrey.pc	CPDAG	Constraint-based 7 Score-based 4 Permutation-based 2 Temporal causal discovery 3 Pairwise direction 3
Several environments Rows from experiments, interventions, or sites, each labeled	CD-NOD andrey.cdnod	CPDAG	Constraint-based 4 Score-based 5 Permutation-based 6
Several datasets One table per group or time point, same columns	Multi-group DirectLiNGAM andrey.multi_group_direct_lingam	DAG	Functional causal models 1 Temporal causal discovery 2
Hidden causes Some common causes are not measured	FCI andrey.fci	PAG	Constraint-based 3 Permutation-based 2 Temporal causal discovery 1 Latent variables 4
Time series One row per time step	PCMCI andrey.pcmci	Temporal graph	Temporal causal discovery 8
Two variables Which one causes the other?	ANM andrey.anm	Two-node DAG	Pairwise direction 3

Methods by family

Constraint-based

9 methods. Start with PC.

Method	Data	Graph	Compared with
PC andrey.pc General-purpose structure learning from i.i.d. observational data	Continuous, categorical, mixed, missing values	CPDAG	causal-learn, gCastle, Tetrad, bnlearn, pcalg, and tigramite 0.1.0, 0.6.0, and 0.8.0 release cards
FCI andrey.fci Structure learning that allows latent confounders and selection bias	Continuous, categorical, mixed, missing values, hidden causes	PAG	causal-learn 0.1.0 and 0.8.0 release cards
GFCI andrey.gfci GES adjacencies, pruned by independence tests and oriented with FCI's rules	Continuous, categorical, mixed, several environments, hidden causes	PAG	Tetrad 0.7.0 release card
CD-NOD andrey.cdnod Constraint-based discovery for data pooled from several domains or regimes	Continuous, categorical, mixed, missing values, several environments	CPDAG	causal-learn 0.7.0 release card
FCI-JCI andrey.fci_jci FCI for data pooled from several domains or regimes, allowing hidden common causes	Continuous, categorical, mixed, missing values, several environments, hidden causes	PAG	pcalg 0.15.0 release card
ICP andrey.icp Invariant causal prediction	Continuous, several environments	DAG	InvariantCausalPrediction 0.14.0 release card
IAMB andrey.iamb One variable's Markov blanket (its parents, children, and children's other parents) by incremental association	Continuous, categorical, mixed, missing values	CPDAG	bnlearn 0.13.0 release card
Inter-IAMB andrey.inter_iamb One variable's Markov blanket by interleaved IAMB, which shrinks after every addition	Continuous, categorical, mixed, missing values	CPDAG	bnlearn 0.12.0 and 0.13.0 release cards
MMPC andrey.mmpc One variable's parents and children, undirected, by max-min parents and children	Continuous, categorical, mixed, missing values	Undirected graph	bnlearn 0.13.0 release card

Score-based

13 methods, 1 experimental. Start with GES.

Method	Data	Graph	Compared with
GES andrey.ges Greedy equivalence search	Continuous, categorical, mixed, missing values, several environments	CPDAG	Tetrad and causal-learn 0.6.0 and 0.7.0 release cards
GIES andrey.gies Greedy interventional equivalence search	Continuous, categorical, mixed, several environments	CPDAG	pcalg 0.7.0 release card
GnIES andrey.gnies Greedy noise-interventional equivalence search	Continuous, several environments	CPDAG	gnies 0.14.0 release card
XGES andrey.xges Extremely greedy equivalence search	Continuous, categorical, mixed	CPDAG	xges 0.3.0 release card
AGES andrey.ages Aggregative greedy equivalence search for linear-Gaussian data with weak edges	Continuous	CPDAG	pcalg 0.17.0 release card
Hill climbing andrey.hc Hill climbing over DAGs	Continuous, categorical, mixed, missing values, several environments	CPDAG	bnlearn and pgmpy 0.3.0 and 0.6.0 release cards
Tabu search andrey.tabu Tabu search over DAGs	Continuous, categorical, mixed, missing values, several environments	CPDAG	bnlearn 0.3.0 release card
Exact search andrey.exact_search Globally optimal score search over DAGs (A* or dynamic programming)	Continuous, categorical, mixed	CPDAG	causal-learn 0.7.0 release card
CALM andrey.calm Continuous-optimization structure learning in the line of NOTEARS	Continuous	DAG	causal-learn 0.7.0 release card
NOTEARS andrey.notears Least squares with an l1 penalty under the acyclicity equation tr(exp(W*W)) = d	Continuous, missing values	DAG	NOTEARS authors' code 0.17.0 release card
DAGMA andrey.dagma Experimental Least squares with an l1 penalty and a log-determinant acyclicity barrier lowered along a central path	Continuous	DAG	Not compared yet
MMHC andrey.mmhc Max-min hill climbing	Continuous, categorical, mixed	CPDAG	bnlearn 0.12.0 and 0.13.0 release cards
RSMAX2 andrey.rsmax2 Conditional-independence tests keep the candidate pairs (restrict=mmpc, iamb, inter_iamb, or pc), then a score search (maximize=hc or tabu) searches DAGs whose edges join only those pairs	Continuous, categorical, mixed	CPDAG	bnlearn 0.12.0 and 0.13.0 release cards

Permutation-based

6 methods. Start with BOSS.

Method	Data	Graph	Compared with
BOSS andrey.boss Best-order score search	Continuous, categorical, mixed, missing values, several environments	CPDAG	causal-learn 0.1.0 and 0.8.0 release cards
GRaSP andrey.grasp Greedy relaxation of the sparsest permutation	Continuous, categorical, mixed, missing values, several environments	CPDAG	causal-learn 0.1.0 and 0.8.0 release cards
BOSS-FCI andrey.boss_fci GFCI with BOSS in place of GES	Continuous, categorical, mixed, several environments, hidden causes	PAG	Tetrad 0.15.0 release card
GRaSP-FCI andrey.grasp_fci GFCI with GRaSP in place of GES	Continuous, categorical, mixed, several environments, hidden causes	PAG	Tetrad 0.15.0 release card
IGSP andrey.igsp Interventional greedy sparsest permutation	Continuous, categorical, mixed, several environments	CPDAG	graphical-model-learning 0.14.0 release card
UT-IGSP andrey.ut_igsp Unknown-target interventional greedy sparsest permutation	Continuous, categorical, mixed, several environments	CPDAG	graphical-model-learning 0.14.0 release card

Functional causal models

7 methods. Start with DirectLiNGAM.

Method	Data	Graph	Compared with
DirectLiNGAM andrey.direct_lingam DirectLiNGAM for linear non-Gaussian data	Continuous	DAG	causal-learn and lingam 0.1.0 and 0.4.1 release cards
ICA-LiNGAM andrey.ica_lingam ICA-based LiNGAM for linear non-Gaussian data	Continuous	DAG	causal-learn 0.1.0 release card
Multi-group DirectLiNGAM andrey.multi_group_direct_lingam DirectLiNGAM fit jointly across >= 2 datasets sharing the same variables	Continuous, several datasets	DAG	lingam 0.7.0 release card
CAM andrey.cam Causal additive model (CAM) for nonlinear additive effects with additive noise	Continuous	DAG	CAM 0.13.0 release card
RESIT andrey.resit Regression with subsequent independence test (RESIT) for nonlinear effects with additive noise of any distribution	Continuous	DAG	authors' R RESIT and lingam 0.13.0 release card
SCORE andrey.score_matching SCORE for nonlinear effects with additive Gaussian noise	Continuous	DAG	SCORE authors' code 0.17.0 release card
NoGAM andrey.nogam NoGAM for nonlinear effects with additive noise of any distribution	Continuous	DAG	dodiscover 0.17.0 release card

Temporal causal discovery

8 methods. Start with PCMCI.

Method	Data	Graph	Compared with
VARMA-LiNGAM andrey.varma_lingam VARMA-LiNGAM for a single multivariate time series	Continuous, time series	Temporal graph	lingam 0.5.0 release card
Longitudinal LiNGAM andrey.longitudinal_lingam Longitudinal LiNGAM for panel data (the same units measured at several time points)	Continuous, several datasets, time series	Temporal graph	lingam 0.5.0 release card
PCMCI andrey.pcmci PCMCI for a single multivariate time series	Continuous, categorical, mixed, missing values, time series	Temporal graph	tigramite 0.5.0 release card
PCMCI+ andrey.pcmciplus PCMCI+ for a single multivariate time series	Continuous, categorical, mixed, missing values, time series	Temporal graph	tigramite 0.5.0 release card
J-PCMCI+ andrey.jpcmciplus J-PCMCI+ for time series from several datasets that differ through measured or hidden contexts	Continuous, several datasets, time series	Temporal graph	tigramite 0.15.0 release card
LPCMCI andrey.lpcmci LPCMCI for a single multivariate time series with possible hidden common causes	Continuous, categorical, mixed, missing values, hidden causes, time series	Temporal graph	tigramite 0.5.0 release card
Granger andrey.granger Granger causality for a single multivariate time series	Continuous, time series	Temporal graph	causal-learn 0.5.0 release card
DYNOTEARS andrey.dynotears DYNOTEARS for a single multivariate time series	Continuous, time series	Temporal graph	CausalNex 0.14.0 release card

Latent variables

4 methods. Start with GIN.

Method	Data	Graph	Compared with
GIN andrey.gin Generalized independent noise (GIN) for linear non-Gaussian models with latent variables	Continuous, hidden causes	DAG	Tetrad and causal-learn 0.7.0 release card
RCD andrey.rcd Repetitive causal discovery (RCD) for linear non-Gaussian data with hidden common causes	Continuous, hidden causes	PAG	lingam 0.2.0 release card
BottomUpParceLiNGAM andrey.bottom_up_parce_lingam BottomUpParceLiNGAM for linear non-Gaussian data with hidden common causes	Continuous, hidden causes	PAG	lingam 0.2.0 release card
CAM-UV andrey.camuv Causal additive models with unobserved variables (CAM-UV) for nonlinear additive effects where some causes are hidden	Continuous, hidden causes	PAG	lingam and causal-learn 0.14.0 release card

Pairwise direction

3 methods. Start with ANM.

Method	Data	Graph	Compared with
ANM andrey.anm Additive-noise-model pairwise direction test	Continuous, missing values, two variables	Two-node DAG	causal-learn 0.4.0 release card
PNL andrey.pnl Post-nonlinear pairwise direction test	Continuous, missing values, two variables	Two-node DAG	causal-learn 0.4.0 release card
LOCI andrey.loci Location-scale-noise-model pairwise direction test	Continuous, missing values, two variables	Two-node DAG	LOCI authors' code 0.16.0 release card