A Conditional Mutual Information Estimator for Mixed Data and an Associated Conditional Independence Test

In this study, we focus on mixed data which are either observations of univariate random variables which can be quantitative or qualitative, or observations of multivariate random variables such that each variable can include both quantitative and qualitative components. We first propose a novel method, called CMIh, to estimate conditional mutual information taking advantages of the previously proposed approaches for qualitative and quantitative data. We then introduce a new local permutation test, called LocAT for local adaptive test, which is well adapted to mixed data. Our experiments illustrate the good behaviour of CMIh and LocAT, and show their respective abilities to accurately estimate conditional mutual information and to detect conditional (in)dependence for mixed data.