A Family of Divergence Measures for Evaluating the Reconstruction Quality of Explainable Ensemble Trees

Validating interpretable surrogate models for ensemble learners requires measuring agreement between the ensemble's internal representation and its surrogate approximation, rather than mere association. Correlation-based approaches are scale-invariant and fail to detect systematic discrepancies in co-occurrence structure. We propose a statistical framework grounded in the agreement-association distinction, centered on the normalized Loss of Interpretability (nLoI). Rooted in the Cressie-Read power divergence family with lambda equal to 2, the nLoI admits a closed-form decomposition into within-node and between-node components, providing a unique diagnostic capability to identify precisely where and why reconstruction fails. The framework incorporates four complementary measures capturing distinct structural facets of approximation quality. A unified permutation testing procedure delivers valid inference for all measures within a single resampling pass. Theoretical properties, including boundedness and symmetry, are established for each metric. Monte Carlo simulations and empirical evaluations confirm exact Type I error control and demonstrate that these measures detect reconstruction fidelity gradients invisible to correlation-based alternatives. The framework is developed and illustrated in the context of Explainable Ensemble Trees (E2Tree), and empirical evaluation on three benchmark datasets illustrates the practical utility of the framework.

Extending Explainable Ensemble Trees (E2Tree) to regression contexts

Ensemble methods such as random forests have transformed the landscape of supervised learning, offering highly accurate prediction through the aggregation of multiple weak learners. However, despite their effectiveness, these methods often lack transparency, impeding users' comprehension of how RF models arrive at their predictions. Explainable ensemble trees (E2Tree) is a novel methodology for explaining random forests, that provides a graphical representation of the relationship between response variables and predictors. A striking characteristic of E2Tree is that it not only accounts for the effects of predictor variables on the response but also accounts for associations between the predictor variables through the computation and use of dissimilarity measures. The E2Tree methodology was initially proposed for use in classification tasks. In this paper, we extend the methodology to encompass regression contexts. To demonstrate the explanatory power of the proposed algorithm, we illustrate its use on real-world datasets.

Decoding Knowledge Claims: The Evaluation of Scientific Publication Contributions through Semantic Analysis

The surge in scientific publications challenges the use of publication counts as a measure of scientific progress, requiring alternative metrics that emphasize the quality and novelty of scientific contributions rather than sheer quantity. This paper proposes the use of Relaxed Word Mover's Distance (RWMD), a semantic text similarity measure, to evaluate the novelty of scientific papers. We hypothesize that RWMD can more effectively gauge the growth of scientific knowledge. To test such an assumption, we apply RWMD to evaluate seminal papers, with Hirsch's H-Index paper as a primary case study. We compare RWMD results across three groups: 1) H-Index-related papers, 2) scientometric studies, and 3) unrelated papers, aiming to discern redundant literature and hype from genuine innovations. Findings suggest that emphasizing knowledge claims offers a deeper insight into scientific contributions, marking RWMD as a promising alternative method to traditional citation metrics, thus better tracking significant scientific breakthroughs.