Massimo Aria

Massimo Aria, Agostino Gnasso, Carmela Iorio

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.

Massimo Aria, Agostino Gnasso, Carmela Iorio et al.

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.

Massimo Aria, Luca D'Aniello, Michelangelo Misuraca et al.

Strategic diagrams and co-word analysis are widely employed to examine the conceptual structure of scientific domains and their development over time. Yet a structural inconsistency characterises dominant longitudinal implementations: themes are detected through relational clustering in weighted networks, whereas their inter-temporal connections are commonly inferred from set-theoretic overlap among keywords or core documents. This study introduces a structurally integrated framework in which lineage reconstruction is embedded within the same weighted relational architecture that underpins cross-sectional detection. The approach models thematic continuity through graded document affiliation and a lineage-strength measure that combines directional coverage with centrality-weighted structural relevance, thereby conceptualising evolution as the reconfiguration of relational structures rather than simple lexical persistence. By aligning thematic detection and temporal modelling within a unified relational paradigm, the framework enhances the methodological coherence and interpretive robustness of longitudinal science mapping.