Understanding the factors that shape students' mathematics performance is vital for designing effective educational policies. This study applies explainable artificial intelligence (XAI) techniques to PISA 2018 data to predict math achievement and identify key predictors across ten countries (67,329 students). We tested four models: Multiple Linear Regression (MLR), Random Forest (RF), CATBoost, and Artificial Neural Networks (ANN), using student, family, and school variables. Models were trained on 70% of the data (with 5-fold cross-validation) and tested on 30%, stratified by country. Performance was assessed with R^2 and Mean Absolute Error (MAE). To ensure interpretability, we used feature importance, SHAP values, and decision tree visualizations. Non-linear models, especially RF and ANN, outperformed MLR, with RF balancing accuracy and generalizability. Key predictors included socio-economic status, study time, teacher motivation, and students' attitudes toward mathematics, though their impact varied across countries. Visual diagnostics such as scatterplots of predicted vs actual scores showed RF and CATBoost aligned closely with actual performance. Findings highlight the non-linear and context-dependent nature of achievement and the value of XAI in educational research. This study uncovers cross-national patterns, informs equity-focused reforms, and supports the development of personalized learning strategies.

We present Uppaal Coshy, a tool for automatic synthesis of a safety strategy -- or shield -- for Markov decision processes over continuous state spaces and complex hybrid dynamics. The general methodology is to partition the state space and then solve a two-player safety game, which entails a number of algorithmically hard problems such as reachability for hybrid systems. The general philosophy of Uppaal Coshy is to approximate hard-to-obtain solutions using simulations. Our implementation is fully automatic and supports the expressive formalism of Uppaal models, which encompass stochastic hybrid automata. The precision of our partition-based approach benefits from using finer grids, which however are not efficient to store. We include an algorithm called Caap to efficiently compute a compact representation of a shield in the form of a decision tree, which yields significant reductions.

Constraint 2b checks the loss of each sample and the derivation is shown as follows. Constraint 2d to 2i are mainly adopted from Bertsimas and Dunn [2019] on Chapter 8.2. Here we briefly explain the meaning and derivations of these constraints. Constraint 2g and 2h are set to ensure that if there's no split on Constraint 2i enforces the hierarchical structure of the tree. Algorithm 1 depicts the details of the Branch-and-bound scheme for training the optimal decision tree.

Variations in complex traits are influenced by multiple genetic variants, environmental risk factors, and their interactions. Though substantial progress has been made in identifying single genetic variants associated with complex traits, detecting the gene-gene and gene-environment interactions remains a great challenge. When a large number of genetic variants and environmental risk factors are involved, searching for interactions is limited to pair-wise interactions due to the exponentially increased feature space and computational intensity. Alternatively, recursive partitioning approaches, such as random forests, have gained popularity in high-dimensional genetic association studies. In this article, we propose a U-Statistic-based random forest approach, referred to as Forest U-Test, for genetic association studies with quantitative traits. Through simulation studies, we showed that the Forest U-Test outperformed existing methods. The proposed method was also applied to study Cannabis Dependence CD, using three independent datasets from the Study of Addiction: Genetics and Environment. A significant joint association was detected with an empirical p-value less than 0.001. The finding was also replicated in two independent datasets with p-values of 5.93e-19 and 4.70e-17, respectively.

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Decision trees offer this inter-pretability, especially when they are small.