Algorithms

Benchpress provides access to a wide range of open-source packages for causal discovery and structure learning such as pcalg, BDgraph, gCastle, TETRAD, bnlearn, causal-learn, and many others, making it easy to use and compare different algorithms within a unified framework. The algorithms are accesed through their corresponding modules, which are listed below. To use an algorithm module, a section with the corresponding name is simply added to the structure_learning_algorithms section of the JSON config file. Sample JSON snippets are provided for each module and you may also review JSON config to see how it works.

The algorithm parameters used in the modules are inherited from the underlying packages as much as possible, maintaining consistency with the original implementations. This means that users familiar with the original packages can easily transfer their knowledge and existing configurations to Benchpress. Users can also refer to the documentation of the underlying packages (linked to in each module) to better understand the parameters and their effects. Apart from the original parameters, each algorithm module is equipped with an additional parameter, timeout, which is the maximum time in seconds allowed for the algorithm to run. After the timeout, the algorithm will be terminated and either an empty file will be created or the current best graph will be saved (if the algorithm supports that).

Modules for MCMC algorithms can be used seamlessly with the other modules. However, apart from the original parameters and timeout, these modules have four additional fields:

• mcmc_seed is the random seed for the algorithm.

• mcmc_estimator specifies which estimator to use (threshold or map).

• threshold specifies the threshold for the posterior edge probabilities if mcmc_estimator is set to threshold.

• burnin_frac is a value in (0, 1) that specifies the fraction of the samples at the beginning of the graph trajectory to be discarded as burn-in.

Algorithm	Package	Graph	Data	MCMC	Edge constraints	Data missingness	Intervention type
ANMNonlinear	gCastle	DAG	C, D
ASOBS	r.blip	DAG	D
BDgraph	BDgraph	UG	C, D, M	Yes		MCAR
BOSS	TETRAD	CPDAG	C, D		Yes
Chordal graph samplers	A. Thomas	DG	C, D	Yes
Corrmat thresh	Benchpress	UG	C
Direct LINGAM	gCastle	DAG	C
Dual PC	dualPC	CG, CPDAG	C
FASK	TETRAD	DAG	C, D		Yes
FGES	TETRAD	CPDAG	C, D		Yes
FOFC	TETRAD	DAG	C, D		Yes
FTFC	TETRAD	DAG	C, D		Yes
Fast IAMB	bnlearn	DAG	C, D, M		Yes
GAE	gCastle	DAG	C
GIES	pcalg	CPDAG	C		Yes		hard
GLasso	scikit-learn	UG	C
GLasso	huge	UG	C
GOBNILP	GOBNILP	DAG	C, D		Yes
GOLEM	gCastle	DAG	C
GRaSP	causal-learn	CPDAG	C, D
GRaSP	TETRAD	CPDAG	C, D		Yes
GS	bnlearn	DAG	C, D, M		Yes
GSP	CausalDAG	DAG	C
GrUES	gues	UDG	C	Yes
GraNDAG	gCastle	DAG	C
H2PC	bnlearn	DAG	C, D, M		Yes
HC	bnlearn	DAG	C, D, M		Yes
HPC	bnlearn	DAG	C, D, M		Yes
IAMB	bnlearn	DAG	C, D, M		Yes
IAMB-FDR	bnlearn	DAG	C, D, M		Yes
ICA-LiNGAM	gCastle	DAG	C
ICA-LiNGAM	TETRAD	DAG	C		Yes
INTER-IAMB	bnlearn	DAG	C, D, M		Yes
Iterative MCMC	BiDAG	DAG, CPDAG	C, D	Yes	Yes
M&B cov est	huge	UG	C
MCSL	gCastle	DAG	C
MICE	mice		C, D, M
MMHC	bnlearn	DAG	C, D, M		Yes
MMPC	bnlearn	DAG	C, D, M		Yes
MVPC	MVPC	CPDAG	C, D		Yes	MAR, MNAR, MCAR
NO TEARS	gCastle	DAG	C
NO TEARS low rank	gCastle	DAG	C
NO TEARS non-linear	gCastle	DAG	C
Order MCMC	BiDAG	DAG, CPDAG	C, D	Yes	Yes
PC	pcalg	CPDAG, CG	C, D		Yes
PC	bnlearn	DAG	C, D, M		Yes
PC	TETRAD	DAG	C, D, M		Yes
PC	gCastle	DAG	C
Parallel DG	parallelDG	DG	C, D	Yes
Particle Gibbs	trilearn	DG	C, D	Yes
Partition MCMC	BiDAG	DAG, CPDAG	C, D	Yes	Yes
Precmat thresh	Benchpress	UG	C
Psi-learning	equSA	UG	C
PyAgrum	pyagrum	DAG	B
RSMAX2	bnlearn	DAG	C, D, M		Yes
S-I HITON-PC	bnlearn	DAG	C, D, M		Yes
TIGER	huge	UG	C
TPC	tpc	CPDAG, MPDAG, TMPDAG	C, D, M		Yes	MAR, MNAR, MCAR
Tabu	bnlearn	DAG	C, D, M		Yes