Generalized Optimal Classification Trees: A Mixed-Integer Programming Approach

Global optimization of decision trees is a long-standing challenge in combinatorial optimization, yet such models play an important role in interpretable machine learning. Although the problem has been investigated for several decades, only recent advances in discrete optimization have enabled practical algorithms for solving optimal classification tree problems on real-world datasets. Mixed-integer programming (MIP) offers a high degree of modeling flexibility, and we therefore propose a MIP-based framework for learning optimal classification trees under nonlinear performance metrics, such as the F1-score, that explicitly addresses class imbalance. To improve scalability, we develop problem-specific acceleration techniques, including a tailored branch-and-cut algorithm, an instance-reduction scheme, and warm-start strategies. We evaluate the proposed approach on 50 benchmark datasets. The computational results show that the framework can efficiently optimize nonlinear metrics while achieving strong predictive performance and reduced solution times compared with existing methods.

A Reproducible Framework for Bias-Resistant Machine Learning on Small-Sample Neuroimaging Data

We introduce a reproducible, bias-resistant machine learning framework that integrates domain-informed feature engineering, nested cross-validation, and calibrated decision-threshold optimization for small-sample neuroimaging data. Conventional cross-validation frameworks that reuse the same folds for both model selection and performance estimation yield optimistically biased results, limiting reproducibility and generalization. Demonstrated on a high-dimensional structural MRI dataset of deep brain stimulation cognitive outcomes, the framework achieved a nested-CV balanced accuracy of 0.660\,$\pm$\,0.068 using a compact, interpretable subset selected via importance-guided ranking. By combining interpretability and unbiased evaluation, this work provides a generalizable computational blueprint for reliable machine learning in data-limited biomedical domains.

Adaptive Evidence Weighting for Audio-Spatiotemporal Fusion

Many machine learning systems have access to multiple sources of evidence for the same prediction target, yet these sources often differ in reliability and informativeness across inputs. In bioacoustic classification, species identity may be inferred both from the acoustic signal and from spatiotemporal context such as location and season; while Bayesian inference motivates multiplicative evidence combination, in practice we typically only have access to discriminative predictors rather than calibrated generative models. We introduce \textbf{F}usion under \textbf{IN}dependent \textbf{C}onditional \textbf{H}ypotheses (\textbf{FINCH}), an adaptive log-linear evidence fusion framework that integrates a pre-trained audio classifier with a structured spatiotemporal predictor. FINCH learns a per-sample gating function that estimates the reliability of contextual information from uncertainty and informativeness statistics. The resulting fusion family \emph{contains} the audio-only classifier as a special case and explicitly bounds the influence of contextual evidence, yielding a risk-contained hypothesis class with an interpretable audio-only fallback. Across benchmarks, FINCH consistently outperforms fixed-weight fusion and audio-only baselines, improving robustness and error trade-offs even when contextual information is weak in isolation. We achieve state-of-the-art performance on CBI and competitive or improved performance on several subsets of BirdSet using a lightweight, interpretable, evidence-based approach. Code is available: \texttt{\href{https://anonymous.4open.science/r/birdnoise-85CD/README.md}{anonymous-repository}}

The Maximum von Neumann Entropy Principle: Theory and Applications in Machine Learning

Von Neumann entropy (VNE) is a fundamental quantity in quantum information theory and has recently been adopted in machine learning as a spectral measure of diversity for kernel matrices and kernel covariance operators. While maximizing VNE under constraints is well known in quantum settings, a principled analogue of the classical maximum entropy framework, particularly its decision theoretic and game theoretic interpretation, has not been explicitly developed for VNE in data driven contexts. In this paper, we extend the minimax formulation of the maximum entropy principle due to Grünwald and Dawid to the setting of von Neumann entropy, providing a game-theoretic justification for VNE maximization over density matrices and trace-normalized positive semidefinite operators. This perspective yields a robust interpretation of maximum VNE solutions under partial information and clarifies their role as least committed inferences in spectral domains. We then illustrate how the resulting Maximum VNE principle applies to modern machine learning problems by considering two representative applications, selecting a kernel representation from multiple normalized embeddings via kernel-based VNE maximization, and completing kernel matrices from partially observed entries. These examples demonstrate how the proposed framework offers a unifying information-theoretic foundation for VNE-based methods in kernel learning.

Multimodal Machine Learning for Integrating Heterogeneous Analytical Systems

Understanding structure-property relationships in complex materials requires integrating complementary measurements across multiple length scales. Here we propose an interpretable "multimodal" machine learning framework that unifies heterogeneous analytical systems for end-to-end characterization, demonstrated on carbon nanotube (CNT) films whose properties are highly sensitive to microstructural variations. Quantitative morphology descriptors are extracted from SEM images via binarization, skeletonization, and network analysis, capturing curvature, orientation, intersection density, and void geometry. These SEM-derived features are fused with Raman indicators of crystallinity/defect states, specific surface area from gas adsorption, and electrical surface resistivity. Multi-dimensional visualization using radar plots and UMAP reveals clear clustering of CNT films according to crystallinity and entanglements. Regression models trained on the multimodal feature set show that nonlinear approaches, particularly XGBoost, achieve the best predictive accuracy under leave-one-out cross-validation. Feature-importance analysis further provides physically meaningful interpretations: surface resistivity is primarily governed by junction-to-junction transport length scales, crystallinity/defect-related metrics, and network connectivity, whereas specific surface area is dominated by intersection density and void size. The proposed multimodal machine learning framework offers a general strategy for data-driven, explainable characterization of complex materials.

Active Transfer Bagging: A New Approach for Accelerated Active Learning Acquisition of Data by Combined Transfer Learning and Bagging Based Models

Modern machine learning has achieved remarkable success on many problems, but this success often depends on the existence of large, labeled datasets. While active learning can dramatically reduce labeling cost when annotations are expensive, early performance is frequently dominated by the initial seed set, typically chosen at random. In many applications, however, related or approximate datasets are readily available and can be leveraged to construct a better seed set. We introduce a new method for selecting the seed data set for active learning, Active-Transfer Bagging (ATBagging). ATBagging estimates the informativeness of candidate data point from a Bayesian interpretation of bagged ensemble models by comparing in-bag and out-of-bag predictive distributions from the labeled dataset, yielding an information-gain proxy. To avoid redundant selections, we impose feature-space diversity by sampling a determinantal point process (DPP) whose kernel uses Random Fourier Features and a quality-diversity factorization that incorporates the informativeness scores. This same blended method is used for selection of new data points to collect during the active learning phase. We evaluate ATBagging on four real-world datasets covering both target-transfer and feature-shift scenarios (QM9, ERA5, Forbes 2000, and Beijing PM2.5). Across seed sizes nseed = 10-100, ATBagging improves or ties early active learning and increases area under the learning-curve relative to alternative seed subset selection methodologies in almost all cases, with strongest benefits in low-data regimes. Thus, ATBagging provides a low-cost, high reward means to initiating active learning-based data collection.

Learning Beyond the Gaussian Data: Learning Dynamics of Neural Networks on an Expressive and Cumulant-Controllable Data Model

We study the effect of high-order statistics of data on the learning dynamics of neural networks (NNs) by using a moment-controllable non-Gaussian data model. Considering the expressivity of two-layer neural networks, we first construct the data model as a generative two-layer NN where the activation function is expanded by using Hermite polynomials. This allows us to achieve interpretable control over high-order cumulants such as skewness and kurtosis through the Hermite coefficients while keeping the data model realistic. Using samples generated from the data model, we perform controlled online learning experiments with a two-layer NN. Our results reveal a moment-wise progression in training: networks first capture low-order statistics such as mean and covariance, and progressively learn high-order cumulants. Finally, we pretrain the generative model on the Fashion-MNIST dataset and leverage the generated samples for further experiments. The results of these additional experiments confirm our conclusions and show the utility of the data model in a real-world scenario. Overall, our proposed approach bridges simplified data assumptions and practical data complexity, which offers a principled framework for investigating distributional effects in machine learning and signal processing.

Predicting Anemia Among Under-Five Children in Nepal Using Machine Learning and Deep Learning

Childhood anemia remains a major public health challenge in Nepal and is associated with impaired growth, cognition, and increased morbidity. Using World Health Organization hemoglobin thresholds, we defined anemia status for children aged 6-59 months and formulated a binary classification task by grouping all anemia severities as \emph{anemic} versus \emph{not anemic}. We analyzed Nepal Demographic and Health Survey (NDHS 2022) microdata comprising 1,855 children and initially considered 48 candidate features spanning demographic, socioeconomic, maternal, and child health characteristics. To obtain a stable and substantiated feature set, we applied four features selection techniques (Chi-square, mutual information, point-biserial correlation, and Boruta) and prioritized features supported by multi-method consensus. Five features: child age, recent fever, household size, maternal anemia, and parasite deworming were consistently selected by all methods, while amenorrhea, ethnicity indicators, and provinces were frequently retained. We then compared eight traditional machine learning classifiers (LR, KNN, DT, RF, XGBoost, SVM, NB, LDA) with two deep learning models (DNN and TabNet) using standard evaluation metrics, emphasizing F1-score and recall due to class imbalance. Among all models, logistic regression attained the best recall (0.701) and the highest F1-score (0.649), while DNN achieved the highest accuracy (0.709), and SVM yielded the strongest discrimination with the highest AUC (0.736). Overall, the results indicate that both machine learning and deep learning models can provide competitive anemia prediction and the interpretable features such as child age, infection proxy, maternal anemia, and deworming history are central for risk stratification and public health screening in Nepal.

Predictive Maintenance for Ultrafiltration Membranes Using Explainable Similarity-Based Prognostics

In reverse osmosis desalination, ultrafiltration (UF) membranes degrade due to fouling, leading to performance loss and costly downtime. Most plants rely on scheduled preventive maintenance, since existing predictive maintenance models, often based on opaque machine learning methods, lack interpretability and operator trust. This study proposes an explainable prognostic framework for UF membrane remaining useful life (RUL) estimation using fuzzy similarity reasoning. A physics-informed Health Index, derived from transmembrane pressure, flux, and resistance, captures degradation dynamics, which are then fuzzified via Gaussian membership functions. Using a similarity measure, the model identifies historical degradation trajectories resembling the current state and formulates RUL predictions as Takagi-Sugeno fuzzy rules. Each rule corresponds to a historical exemplar and contributes to a transparent, similarity-weighted RUL estimate. Tested on 12,528 operational cycles from an industrial-scale UF system, the framework achieved a mean absolute error of 4.50 cycles, while generating interpretable rule bases consistent with expert understanding.

PyGALAX: An Open-Source Python Toolkit for Advanced Explainable Geospatial Machine Learning

PyGALAX is a Python package for geospatial analysis that integrates automated machine learning (AutoML) and explainable artificial intelligence (XAI) techniques to analyze spatial heterogeneity in both regression and classification tasks. It automatically selects and optimizes machine learning models for different geographic locations and contexts while maintaining interpretability through SHAP (SHapley Additive exPlanations) analysis. PyGALAX builds upon and improves the GALAX framework (Geospatial Analysis Leveraging AutoML and eXplainable AI), which has proven to outperform traditional geographically weighted regression (GWR) methods. Critical enhancements in PyGALAX from the original GALAX framework include automatic bandwidth selection and flexible kernel function selection, providing greater flexibility and robustness for spatial modeling across diverse datasets and research questions. PyGALAX not only inherits all the functionalities of the original GALAX framework but also packages them into an accessible, reproducible, and easily deployable Python toolkit while providing additional options for spatial modeling. It effectively addresses spatial non-stationarity and generates transparent insights into complex spatial relationships at both global and local scales, making advanced geospatial machine learning methods accessible to researchers and practitioners in geography, urban planning, environmental science, and related fields.