In this paper, we consider a perturbation-based metric of predictive faithfulness of feature rankings (or attributions) that we call PGI squared When applied to decision tree-based regression models, the metric can be computed exactly and efficiently for arbitrary independent feature perturbation distributions. In particular, the computation does not involve Monte Carlo sampling that has been typically used for computing similar metrics and which is inherently prone to inaccuracies. As a second contribution, we proposed a procedure for constructing feature ranking based on PGI squared. Our results indicate the proposed ranking method is comparable to the widely recognized SHAP explainer, offering a viable alternative for assessing feature importance in tree-based models.

Neural causal discovery methods have recently improved in terms of scalability and computational efficiency. However, our systematic evaluation highlights significant room for improvement in their accuracy when uncovering causal structures. We identify a fundamental limitation: unavoidable likelihood score estimation errors disallow distinguishing the true structure, even for small graphs and relatively large sample sizes. Furthermore, we identify the faithfulness property as a critical bottleneck: (i) it is likely to be violated across any reasonable dataset size range, and (ii) its violation directly undermines the performance of neural penalized-likelihood discovery methods. These findings lead us to conclude that progress within the current paradigm is fundamentally constrained, necessitating a paradigm shift in this domain.