Causal machine learning (ML) promises to provide powerful tools for estimating individual treatment effects. While causal methods have placed some emphasis on heterogeneity in treatment response, it is of paramount importance to clarify the nature of this heterogeneity, by highlighting which variables drive it. We propose PermuCATE, an algorithm based on the Conditional Permutation Importance (CPI) method, for statistically rigorous global variable importance assessment in the estimation of the Conditional Average Treatment Effect (CATE). Theoretical analysis of the finite sample regime and empirical studies show that PermuCATE has lower variance than the Leave-One-Covariate-Out (LOCO) method and provides a reliable measure of variable importance. This property increases statistical power, which is crucial for causal inference applications with finite sample sizes. We empirically demonstrate the benefits of PermuCATE in simulated and real datasets, including complex settings with high-dimensional, correlated variables.

A novel neuro-fuzzy approach to nonlinear dimensionality reduction is proposed. The approach is an auto-associative modification of the Neuro-Fuzzy Kolmogorov's Network (NFKN) with a “bottleneck” hidden layer. Two training algorithms are considered. The validity of theoretical results and the advantages of the proposed model are confirmed by an experiment in nonlinear principal component analysis and an application in the visualization of high-dimensional wastewater treatment plant data.