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.

翻译：条件独立性检验（CIT）是机器学习中的常见任务，例如用于变量选择，也是基于约束的因果发现的主要组成部分。尽管当前大多数CIT方法假设所有变量均为数值型或所有变量均为分类型，但许多实际应用涉及包含数值型和分类型变量的混合型数据集。非参数CIT可通过结合局部置换方案的条件互信息（CMI）估计器实现。近期，两种基于k近邻（k-NN）的混合型数据集CMI估计器被提出。与任何k-NN方法一样，这些估计器依赖于距离度量的定义。一种方法通过分类变量的一热编码计算距离，本质上将分类变量视为离散数值变量；另一种方法则通过熵项表达CMI，其中分类变量仅作为条件出现。本文研究了这些估计器，并提出前一种方法的变体——不将分类变量视为数值变量。数值实验表明，我们的变体在不同数据分布和预处理类型下能更稳健地检测依赖关系。