Meta-Dependence in Conditional Independence Testing
Constraint-based causal discovery algorithms utilize many statistical tests for conditional independence to uncover networks of causal dependencies. These approaches to causal discovery rely on an assumed correspondence between the graphical properties of a causal structure and the conditional independence properties of observed variables, known as the causal Markov condition and faithfulness. Finite data yields an empirical distribution that is "close" to the actual distribution. Across these many possible empirical distributions, the correspondence to the graphical properties can break down for different conditional independencies, and multiple violations can occur at the same time. We study this "meta-dependence" between conditional independence properties using the following geometric intuition: each conditional independence property constrains the space of possible joint distributions to a manifold. The "meta-dependence" between conditional independences is informed by the position of these manifolds relative to the true probability distribution. We provide a simple-to-compute measure of this meta-dependence using information projections and consolidate our findings empirically using both synthetic and real-world data.
Code (0)
등록된 구현이 없습니다.
Tasks
Causal DiscoverySimilar Papers 제목 키워드 기반
Conditional Independence Test Based on Transport Maps
Testing conditional independence between two random vectors given a third is a fundamental and challenging problem in statistics, particularly in multivariate nonparametric settings due to the complexity of conditional s…
Kernel-based Conditional Independence Test and Application in Causal Discovery
Conditional independence testing is an important problem, especially in Bayesian network learning and causal discovery. Due to the curse of dimensionality, testing for conditional independence of continuous variables is …
Causal DiscoveryPredictive Independence Testing, Predictive Conditional Independence Testing, and Predictive Graphical Modelling
Testing (conditional) independence of multivariate random variables is a task central to statistical inference and modelling in general - though unfortunately one for which to date there does not exist a practicable work…
PhilosophyConditional Local Independence Testing with Application to Dynamic Causal Discovery
In this note, we extend the conditional local independence testing theory developed in Christgau et al. (2024) to Ito processes. The result can be applied to causal discovery in dynamic systems.
Causal DiscoveryPractical Kernel Tests of Conditional Independence
We describe a data-efficient, kernel-based approach to statistical testing of conditional independence. A major challenge of conditional independence testing, absent in tests of unconditional independence, is to obtain t…