Conditional association

Estimating conditional dependence between two random variables given the knowledge of a third random variable is essential in neuroscientific applications to understand the causal architecture of a distributed network. However, existing methods of assessing conditional dependence, such as the conditional mutual information, are computationally expensive, involve free parameters, and are difficult to understand in the context of realizations. In this letter, we discuss a novel approach to this problem and develop a computationally simple and parameter-free estimator. The difference between the proposed approach and the existing ones is that the former expresses conditional dependence in terms of a finite set of realizations, whereas the latter use random variables, which are not available in practice. We call this approach conditional association, since it is based on a generalization of the concept of association to arbitrary metric spaces. We also discuss a novel and computationally efficient approach of generating surrogate data for evaluating the significance of the acquired association value.