constraint-based
Definition
Constraint-based refers to a class of causal discovery methods that use patterns of statistical independence and dependence estimated from observational data to infer causal structures among variables. These methods operate by applying criteria such as d-separation to determine which conditional independencies are present in the data, then identifying the causal graph consistent with those patterns. A key practical advantage is that they require only a single observational dataset, unlike invariance-based approaches that demand multiple datasets collected under different experimental conditions. The most widely studied constraint-based methods assume acyclicity, meaning that if X causes Y, then Y cannot cause X, an assumption that is problematic for psychological phenomena such as psychopathologies where feedback loops between symptoms are theoretically expected. Cyclic constraint-based algorithms have been developed to address this limitation, and their performance in psychological research contexts, including their behavior under varying sample sizes, network densities, and the presence of unobserved confounders, has been evaluated through simulation.
Sources: Park et al. (2024)
Related Terms
- cyclic causal discovery (1 shared article)
- directed cyclic graph (DCG) (1 shared article)
- partial ancestral graph (PAG) (1 shared article)
- statistical network model (1 shared article)
Applications
Constraint-based and Cyclic Causal Discovery
Constraint-based methods have been extended to handle directed cyclic graphs, in which reciprocal causal relationships between variables are permitted. In psychological research, phenomena such as depression involve feedback loops, for example between perceived stress, negative affect, and rumination, that cannot be captured by acyclic models alone. Cyclic constraint-based algorithms evaluated through simulation work on cross-sectional data can in principle recover such structures, though interpreting their output is more demanding than for their acyclic counterparts because a given pattern of statistical dependence does not map unambiguously onto a direct causal link in a cyclic graph.
Sources: Park et al. (2024)
Constraint-based and Statistical Network Models
Statistical network models such as the Gaussian Graphical Model are built on undirected Pairwise Markov Random Fields, in which edges represent conditional statistical associations rather than directed causal effects. Researchers have proposed replacing these models with purpose-built constraint-based causal discovery methods when the goal is to recover the underlying causal structure from observational data, because network edges may reflect inferential artefacts such as conditioning on common effects rather than direct causal relationships.
Sources: Park et al. (2024)
