A kernel conditional independence test for relational data

Conditional independence (CI) tests play a central role in statistical inference, machine learning, and causal discovery. Most existing CI tests assume that the samples are independently and identically distributed (i.i.d.). However, this assumption often does not hold in the case of relational data. We define Relational Conditional Independence (RCI), a generalization of CI to the relational setting. We show how, under a set of structural assumptions, we can test for RCI by reducing the task of testing for RCI on non-i.i.d. data to the problem of testing for CI on several data sets each of which consists of i.i.d. samples. We develop Kernel Relational CI test (KRCIT), a nonparametric test as a practical approach to testing for RCI by relaxing the structural assumptions used in our analysis of RCI. We describe results of experiments with synthetic relational data that show the benefits of KRCIT relative to traditional CI tests that don't account for the non-i.i.d. nature of relational data.