Meta-Dependence in Conditional Independence Testing

2025-04-17

AI Summary

This paper addresses the failure of conditional independence (CI) tests in constraint-based causal discovery under limited samples. We introduce “meta-dependence”—a phenomenon wherein multiple CI hypotheses jointly fail due to the geometric relationship between the true data distribution and the CI manifold. Methodologically, within an information-geometric framework, we construct a computable meta-dependence strength measure based on KL-divergence projections onto the CI manifold, explicitly capturing how the distribution’s position relative to the manifold governs test robustness. Our contributions are threefold: (i) the first formal characterization of the meta-dependence mechanism; (ii) a theoretical foundation for CI test reliability under manifold constraints; and (iii) a practical metric that significantly improves stability in causal structure learning—especially in small-sample and high-dimensional regimes. Empirical evaluation demonstrates accurate prediction of CI test failure patterns, with average error reduced by 37%.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI

Abstract

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.

Problem

• Study meta-dependence in conditional independence testing
• Measure impact of empirical distributions on graphical properties
• Propose computable metric for conditional independence manifold relations

Innovation

• Geometric intuition for conditional independence manifolds
• Information projections measure meta-dependence
• Empirical validation with synthetic and real data