From Conditional to Unconditional Independence: Testing Conditional Independence via Transport Maps
This addresses a fundamental challenge in statistics for researchers and practitioners dealing with complex conditional structures, though it appears incremental as it builds on existing transport map and normalizing flow techniques.
The paper tackles the problem of testing conditional independence in multivariate nonparametric statistics by transforming it into an unconditional independence test using transport maps estimated with conditional continuous normalizing flows, and demonstrates its effectiveness through simulations and real-data analysis.
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 structures. We propose a novel method for testing conditional independence by transforming it to an unconditional independence test problem. We achieve this by constructing two transport maps that transform conditional independence into unconditional independence, this substantially simplifies the problem. These transport maps are estimated from data using conditional continuous normalizing flow models. Within this framework, we derive a test statistic and prove its asymptotic validity under both the null and alternative hypotheses. A permutation-based procedure is employed to evaluate the significance of the test. We validate the proposed method through extensive simulations and real-data analysis. Our numerical studies demonstrate the practical effectiveness of the proposed method for conditional independence