A new nonparametric measure of conditional independence

In this paper we propose a new measure of conditional independence that is loosely based on measuring the L₂ distance between the conditional joint and the product of the conditional marginal density functions. However, we propose to smooth the arguments prior to measuring the distance and use kernel density estimation to derive the estimator. We show that under suitable conditions the proposed smoothing does not affect the conditional independence but using proper smoothing function helps in choosing the bandwidth parameter robustly. We discuss the computational issues and propose an approximation to evaluate the estimator efficiently. We apply the proposed measure in different experiments to show its validity.