HC-STABLE Algorithm

Overview

HC-Stable is a variant of the hill-climbing algorithm designed to produce results that are reproducible across different variable orderings and implementations. Standard HC is order-sensitive: when two candidate moves yield identical score improvements the winner depends on the iteration order, which can vary between runs or platforms. HC-Stable breaks these ties deterministically using a canonical ordering, so the same data always produces the same graph.

The stability guarantee makes HC-Stable particularly valuable for reproducibility studies, benchmarking, and any application where consistent results across re-runs or across machines are required. Runtime is comparable to standard HC.

Class: score · DAG Package: CausalIQ

Reference

Kitson N.K. and Constantinou A.C. (2025) – Stable structure learning with HC- Stable and Tabu-Stable algorithms. Int. J. Approx. Reason. 186, 109522. https://doi.org/10.1016/j.ijar.2025.109522

Hyperparameters

Hyperparameter	Type	Default	Values	Description
iss	float	1.0	—	Imaginary Sample Size weighting the prior in Bayesian scores.
max_elapsed	int	No limit	—	Maximum allowed execution time in seconds.
max_iterations	int	No limit	—	Maximum number of iterations.
penalty_weight	float	1.0	—	Weight of the penalty component in AIC and BIC scores.
score	str	bic	aic, bdeu, bge, bic, k2, loglik	Scoring function for score-based learning.

Variants

Variant	Package
causaliq	CausalIQ