Flow Matching based Conditional Independence Tests and Causal Structure Learning

Constraint-based causal discovery methods require a large number of conditional independence (CI) tests, which severely limits their practical applicability due to high computational complexity. Therefore, it is crucial to design an algorithm that both reduce the number of required CI tests and accelerate each individual test. To this end, we propose a Flow Matching–based Conditional Independence Test (FMCIT). The proposed test effectively controls the type I error and maintains high testing power under the alternative hypothesis, even in the presence of high-dimensional conditioning sets. In addition, the method leverages the high computational efficiency of flow matching and requires training the model only once throughout the entire causal discovery procedure, thereby substantially accelerating causal discovery. We further integrate FMCIT into a two-stage guided PC skeleton learning framework, termed GPC-FMCIT, which combines fast screening with guided, budgeted refinement using FMCIT. This design yields explicit bounds on the number of CI queries while maintaining high statistical power. Experiments on synthetic and real-world data demonstrate favorable accuracy--efficiency trade-offs over existing CI testing methods and PC variants.