Meta-Dependence in Conditional Independence Testing
This addresses a foundational issue in causal discovery algorithms for researchers, but it is incremental as it builds on existing geometric intuitions.
The paper tackles the problem of meta-dependence between conditional independence properties in causal discovery, which can lead to violations in graphical assumptions with finite data, and provides a computable measure using information projections, validated empirically on synthetic and real-world datasets.
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.