  Conditional independence testing (CIT) is a common task in machine learning,
e.g., for variable selection, and a main component of constraint-based causal
discovery. While most current CIT approaches assume that all variables are
numerical or all variables are categorical, many real-world applications
involve mixed-type datasets that include numerical and categorical variables.
Non-parametric CIT can be conducted using conditional mutual information (CMI)
estimators combined with a local permutation scheme. Recently, two novel CMI
estimators for mixed-type datasets based on k-nearest-neighbors (k-NN) have
been proposed. As with any k-NN method, these estimators rely on the definition
of a distance metric. One approach computes distances by a one-hot encoding of
the categorical variables, essentially treating categorical variables as
discrete-numerical, while the other expresses CMI by entropy terms where the
categorical variables appear as conditions only. In this work, we study these
estimators and propose a variation of the former approach that does not treat
categorical variables as numeric. Our numerical experiments show that our
variant detects dependencies more robustly across different data distributions
and preprocessing types.
