Extending PPCEF: probabilistically plausible counterfactual explanations for regression and heterogeneous tabular data

Abstract The contribution of PPCEF, introduced in our earlier conference paper, generates probabilistically plausible counterfactual explanations for differentiable classifiers on numerical tabular data by combining an unconstrained optimization objective with conditional Normalizing Flow density estimation. This article extends that framework in three directions. First, it adapts the validity objective to regression, enabling counterfactuals to target continuous outcomes while satisfying a density-based plausibility condition. Second, it supports heterogeneous tabular data through dequantization, Gumbel-Softmax relaxation, and post-optimization quantization of categorical features. Third, it incorporates optional actionability constraints for immutable and monotonic features. We evaluate the regression and mixed-data extensions on five additional mixed-type classification datasets and five regression datasets, using linear and non-linear predictors and corresponding mixed-data and regression baselines, and provide new regression-regularization and density-threshold sensitivity analyses. Across the added settings, PPCEF generally achieves high validity and probabilistic plausibility.