Agostino Gnasso|

Saltwater intrusion is a recurrent environmental hazard for Mediterranean coastal systems, and identifying which physico-chemical variables track salinity is central to monitoring design. Estimating such associations from depth-resolved profiles requires two features of the data to be addressed: the uncertainty of each depth-bin summary, arising from pooling readings taken at several stations along a steep longitudinal gradient, and the residual vertical dependence left after conditioning on the covariates. This paper proposes a Bayesian errors-in-variables-like model with a Gaussian process component for residual depth structure, applied to two synoptic campaigns in the Volturno River mouth (Italy) under contrasting winter and summer hydrological conditions. The results show that temperature is consistently associated with salinity, but the sign of the association differs between the two seasonal conditions during sampling: it is positive in winter and negative in summer within the reach occupied by the salt wedge. Dissolved oxygen is important in winter only. The residual depth amplitude is small in both campaigns, while the complementary full river reach analysis for the summer campaign yields a substantially larger residual depth component, showing that the fitted relationship is sensitive to the sampled river reach. Under near-perfect collinearity the ordering of the covariates is better identified than any individual coefficient, and is reported through posterior rank probabilities. A simulation study shows that the specification maintains nominal credible-interval coverage where a naive regression collapses to a few per cent and reverses a tracer coefficient’s sign in up to 45 per cent of replicates. Cross-validation on held-out depth bins supports predictive adequacy within each campaign, while over comparable river reaches the estimated relationships are specific to the contrasting hydrological regimes represented by the two campaigns and do not transfer between them.

The advent of ensemble methods, such as Random Forest (RF), has led to a paradigm shift in supervised learning. These methods have achieved remarkable levels of prediction accuracy by aggregating multiple weak learners. However, a drawback of these methods is their lack of transparency, which often prevents users from understanding their prediction processes. In light of these challenges, Explainable Ensemble Trees (E2Tree) has recently been proposed, providing a graphical representation of the relationships between response variables and predictors in RFs for classification. E2Tree constructs a single decision tree based on (dis)similarities between observations. By summarizing both distances in terms of predictors and a forest as a single decision tree, E2Tree merges the strengths of both decision trees and decision tree ensembles. In this paper, we propose to extend the E2Tree methodology to regression contexts. We investigate the performance of E2Tree for regression using real‐world datasets. We use the Mantel test to test the correlation between similarities of the RF and E2Tree.

Machine Learning techniques are celebrated for their predictive accuracy, uncovering subtle patterns beyond human perception. Among these, Random Forest is a widely adopted ensemble method, valued for its robust performance and ease of use, especially in scenarios where the cost of errors is significant. However, the inherent opacity of such models raises concerns about their interpretability and trustworthiness. In this study, we apply the Random Forest algorithm to analyze data from the Italian National Institute of Statistics (Istituto Nazionale di Statistica, Istat), specifically the European Health Interview Survey (EHIS), to identify risk factors associated with depression in Italy. To enhance transparency and interpretability, we subsequently employ the Explainable Ensemble Trees methodology to explore and understand the decision-making processes of the Random Forest model. The goal is to demonstrate how E2Tree can provide actionable insights for targeted interventions, supporting public health efforts in addressing mental health challenges.

The growing success of Machine Learning (ML) is making significant improvements to predictive models, facilitating their integration in various application fields. Despite its growing success, there are some limitations and disadvantages: the most significant is the lack of interpretability that does not allow users to understand how particular decisions are made. Our study focus on one of the best performing and most used models in the Machine Learning framework, the Random Forest model. It is known as an efficient model of ensemble learning, as it ensures high predictive precision, flexibility, and immediacy; it is recognized as an intuitive and understandable approach to the construction process, but it is also considered a Black Box model due to the large number of deep decision trees produced within it. The aim of this research is twofold. We present a survey about interpretative proposal for Random Forest and then we perform a machine learning experiment providing a comparison between two methodologies, inTrees, and NodeHarvest, that represent the main approaches in the rule extraction framework. The proposed experiment compares methods performance on six real datasets covering different data characteristics: n. of observations, balanced/unbalanced response, the presence of categorical and numerical predictors. This study contributes to picture a review of the methods and tools proposed for ensemble tree interpretation, and identify, in the class of rule extraction approaches, the best proposal.

BACKGROUND: The wellbeing of oral lichen planus patients (OLPs) may be strongly influenced by a poor quality of sleep (QoS) and psychological impairment. The aims were to analyze the prevalence of sleep disturbance, anxiety, and depression in OLPs and to validate the Pittsburgh Sleep Quality Index (PSQI) in OLPs. METHODS: Three hundred keratotic OLPs (K-OLPs), 300 with predominant non-keratotic OLP (nK-OLPs), and 300 controls were recruited in 15 Italian universities. The PSQI, Epworth Sleepiness Scale (ESS), Hamilton Rating Scales for Depression and Anxiety (HAM-D and HAM-A), Numeric Rating Scale (NRS), and Total Pain Rating Index (T-PRI) were administered. RESULTS: Oral lichen planus patients had statistically higher scores than the controls in the majority of the PSQI sub-items (p-values < 0.001**). Moreover, OLPs had higher scores in the HAM-D, HAM-A, NRS, and T-PRI (p-values < 0.001**). No differences in the PSQI sub-items' scores were found between the K-OLPs and nK-OLPs, although nK-OLPs suffered from higher levels of anxiety, depression, and pain (p-values: HAM-A, 0.007**, HAM-D, 0.009**, NRS, <0.001**, T-PRI, <0.001**). The female gender, anxiety, depression (p-value: 0.007**, 0.001**, 0.020*) and the intensity of pain, anxiety, and depression (p-value: 0.006**, <0.001**, 0.014*) were independent predictors of poor sleep (PSQI > 5) in K-OLPs and nK-OLPs, respectively. The PSQI's validation demonstrated good internal consistency and reliability of both the total and subscale of the PSQI. CONCLUSIONS: The OLPs reported an overall impaired QoS, which seemed to be an independent parameter according to the regression analysis. Hence, clinicians should assess QoS in OLPs and treat sleep disturbances in order to improve OLPs management.