Random Forests and Gradient Boosting are among the most effective algorithms for supervised learning on tabular data. Both belong to the class of tree-based ensemble methods, where predictions are obtained by aggregating many randomized regression trees. In this paper, we develop a theoretical framework for analyzing such methods through Reproducing Kernel Hilbert Spaces (RKHSs) constructed on tree ensembles--more precisely, on the random partitions generated by randomized regression trees. We establish fundamental analytical properties of the resulting Random Forest kernel, including boundedness, continuity, and universality, and show that a Random Forest predictor can be characterized as the unique minimizer of a penalized empirical risk functional in this RKHS, providing a variational interpretation of ensemble learning. We further extend this perspective to the continuous-time formulation of Gradient Boosting introduced by Dombry and Duchamps (2024a,b), and demonstrate that it corresponds to a gradient flow on a Hilbert manifold induced by the Random Forest RKHS. A key feature of this framework is that both the kernel and the RKHS geometry are data-dependent, offering a theoretical explanation for the strong empirical performance of tree-based ensembles. Finally, we illustrate the practical potential of this approach by introducing a kernel principal component analysis built on the Random Forest kernel, which enhances the interpretability of ensemble models, as well as GVI, a new geometric variable importance criterion.

Modern artificial intelligence systems make critical decisions yet often fail silently when uncertain -- even well-calibrated models provide no mechanism to identify \textit{which specific predictions} are unreliable. We develop a geometric framework addressing both calibration and instance-level uncertainty quantification for neural network probability outputs. Treating probability vectors as points on the $(c-1)$-dimensional probability simplex equipped with the Fisher--Rao metric, we construct: (i) Additive Log-Ratio (ALR) calibration maps that reduce exactly to Platt scaling for binary problems while extending naturally to multi-class settings, and (ii) geometric reliability scores that translate calibrated probabilities into actionable uncertainty measures, enabling principled deferral of ambiguous predictions to human review. Theoretical contributions include: consistency of the calibration estimator at rate $O_p(n^{-1/2})$ via M-estimation theory (Theorem~1), and tight concentration bounds for reliability scores with explicit sub-Gaussian parameters enabling sample size calculations for validation set design (Theorem~2). We conjecture Neyman--Pearson optimality of our neutral zone construction based on connections to Bhattacharyya coefficients. Empirical validation on Adeno-Associated Virus classification demonstrates that the two-stage framework captures 72.5\% of errors while deferring 34.5\% of samples, reducing automated decision error rates from 16.8\% to 6.9\%. Notably, calibration alone yields marginal accuracy gains; the operational benefit arises primarily from the reliability scoring mechanism, which applies to any well-calibrated probability output. This work bridges information geometry and statistical learning, offering formal guarantees for uncertainty-aware classification in applications requiring rigorous validation.

Feature selection has remained a daunting challenge in machine learning and artificial intelligence, where increasingly complex, high-dimensional datasets demand principled strategies for isolating the most informative predictors. Despite widespread adoption, many established techniques suffer from notable limitations; some incur substantial computational cost, while others offer no definite statistical driven stopping criteria or assesses the significance of their importance scores. A common heuristic approach introduces multiple random noise features and retains all predictors ranked above the strongest noise feature. Although intuitive, this strategy lacks theoretical justification and depends heavily on heuristics. This paper proposes a novel feature selection method that addresses these limitations. Our approach introduces multiple random noise features and evaluates each feature's importance against the maximum importance value among these noise features incorporating a non-parametric bootstrap-based hypothesis testing framework to establish a solid theoretical foundation. We establish the conceptual soundness of our approach through statistical derivations that articulate the principles guiding the design of our algorithm. To evaluate its reliability, we generated simulated datasets under controlled statistical settings and benchmarked performance against Boruta and Knockoff-based methods, observing consistently stronger recovery of meaningful signal. As a demonstration of practical utility, we applied the technique across diverse real-world datasets, where it surpassed feature selection techniques including Boruta, RFE, and Extra Trees. Hence, the method emerges as a robust algorithm for principled feature selection, enabling the distillation of informative predictors that support reliable inference, enhanced predictive performance, and efficient computation.

Streaming video understanding requires models not only to process temporally incoming frames, but also to anticipate user intention for realistic applications like AR glasses. While prior streaming benchmarks evaluate temporal reasoning, none measure whether MLLMs can interpret or leverage human gaze signals within a streaming setting. To fill this gap, we introduce StreamGaze, the first benchmark designed to evaluate how effectively MLLMs use gaze for temporal and proactive reasoning in streaming videos. StreamGaze introduces gaze-guided past, present, and proactive tasks that comprehensively evaluate streaming video understanding. These tasks assess whether models can use real-time gaze to follow shifting attention and infer user intentions from only past and currently observed frames. To build StreamGaze, we develop a gaze-video QA generation pipeline that aligns egocentric videos with raw gaze trajectories via fixation extraction, region-specific visual prompting, and scanpath construction. This pipeline produces spatio-temporally grounded QA pairs that closely reflect human perceptual dynamics. Across all StreamGaze tasks, we observe substantial performance gaps between state-of-the-art MLLMs and human performance, revealing fundamental limitations in gaze-based temporal reasoning, intention modeling, and proactive prediction. We further provide detailed analyses of gaze-prompting strategies, reasoning behaviors, and task-specific failure modes, offering deeper insight into why current MLLMs struggle and what capabilities future models must develop. All data and code will be publicly released to support continued research in gaze-guided streaming video understanding.

Deep unsupervised anomaly detection in brain magnetic resonance imaging offers a promising route to identify pathological deviations without requiring lesion-specific annotations. Yet, fragmented evaluations, heterogeneous datasets, and inconsistent metrics have hindered progress toward clinical translation. Here, we present a large-scale, multi-center benchmark of deep unsupervised anomaly detection for brain imaging. The training cohort comprised 2,976 T1 and 2,972 T2-weighted scans from healthy individuals across six scanners, with ages ranging from 6 to 89 years. Validation used 92 scans to tune hyperparameters and estimate unbiased thresholds. Testing encompassed 2,221 T1w and 1,262 T2w scans spanning healthy datasets and diverse clinical cohorts. Across all algorithms, the Dice-based segmentation performance varied between 0.03 and 0.65, indicating substantial variability. To assess robustness, we systematically evaluated the impact of different scanners, lesion types and sizes, as well as demographics (age, sex). Reconstruction-based methods, particularly diffusion-inspired approaches, achieved the strongest lesion segmentation performance, while feature-based methods showed greater robustness under distributional shifts. However, systematic biases, such as scanner-related effects, were observed for the majority of algorithms, including that small and low-contrast lesions were missed more often, and that false positives varied with age and sex. Increasing healthy training data yields only modest gains, underscoring that current unsupervised anomaly detection frameworks are limited algorithmically rather than by data availability. Our benchmark establishes a transparent foundation for future research and highlights priorities for clinical translation, including image native pretraining, principled deviation measures, fairness-aware modeling, and robust domain adaptation.

Failing to be aware of speeding vehicles approaching from behind poses a huge threat to the road safety of pedestrians and cyclists. In this paper, we propose BlinkBud, which utilizes a single earbud and a paired phone to online detect hazardous objects approaching from behind of a user. The core idea is to accurately track visually identified objects utilizing a small number of sampled camera images taken from the earbud. To minimize the power consumption of the earbud and the phone while guaranteeing the best tracking accuracy, a novel 3D object tracking algorithm is devised, integrating both a Kalman filter based trajectory estimation scheme and an optimal image sampling strategy based on reinforcement learning. Moreover, the impact of constant user head movements on the tracking accuracy is significantly eliminated by leveraging the estimated pitch and yaw angles to correct the object depth estimation and align the camera coordinate system to the user's body coordinate system, respectively. We implement a prototype BlinkBud system and conduct extensive real-world experiments. Results show that BlinkBud is lightweight with ultra-low mean power consumptions of 29.8 mW and 702.6 mW on the earbud and smartphone, respectively, and can accurately detect hazards with a low average false positive ratio (FPR) and false negative ratio (FNR) of 4.90% and 1.47%, respectively.

Stroke is a major cause of death and permanent impairment, making it a major worldwide health concern. For prompt intervention and successful preventative tactics, early risk assessment is essential. To address this challenge, we used ensemble modeling and explainable AI (XAI) techniques to create an interpretable machine learning framework for stroke risk prediction. A thorough evaluation of 10 different machine learning models using 5-fold cross-validation across several datasets was part of our all-inclusive strategy, which also included feature engineering and data pretreatment (using Random Over-Sampling (ROS) to solve class imbalance). Our optimized ensemble model (Random Forest + ExtraTrees + XGBoost) performed exceptionally well, obtaining a strong 99.09% accuracy on the Stroke Prediction Dataset (SPD). We improved the model's transparency and clinical applicability by identifying three important clinical variables using LIME-based interpretability analysis: age, hypertension, and glucose levels. Through early prediction, this study highlights how combining ensemble learning with explainable AI (XAI) can deliver highly accurate and interpretable stroke risk assessment. By enabling data-driven prevention and personalized clinical decisions, our framework has the potential to transform stroke prediction and cardiovascular risk management.

The precise segmentation of intracranial aneurysms and their parent vessels (IA-Vessel) is a critical step for hemodynamic analyses, which mainly depends on computational fluid dynamics (CFD). However, current segmentation methods predominantly focus on image-based evaluation metrics, often neglecting their practical effectiveness in subsequent CFD applications. To address this deficiency, we present the Intracranial Aneurysm Vessel Segmentation (IAVS) dataset, the first comprehensive, multi-center collection comprising 641 3D MRA images with 587 annotations of aneurysms and IA-Vessels. In addition to image-mask pairs, IAVS dataset includes detailed hemodynamic analysis outcomes, addressing the limitations of existing datasets that neglect topological integrity and CFD applicability. To facilitate the development and evaluation of clinically relevant techniques, we construct two evaluation benchmarks including global localization of aneurysms (Stage I) and fine-grained segmentation of IA-Vessel (Stage II) and develop a simple and effective two-stage framework, which can be used as a out-of-the-box method and strong baseline. For comprehensive evaluation of applicability of segmentation results, we establish a standardized CFD applicability evaluation system that enables the automated and consistent conversion of segmentation masks into CFD models, offering an applicability-focused assessment of segmentation outcomes. The dataset, code, and model will be public available at https://github.com/AbsoluteResonance/IAVS.

As a variant of the Area Under the ROC Curve (AUC), the partial AUC (PAUC) focuses on a specific range of false positive rate (FPR) and/or true positive rate (TPR) in the ROC curve. It is a pivotal evaluation metric in real-world scenarios with both class imbalance and decision constraints. However, selecting instances within these constrained intervals during its calculation is NP-hard, and thus typically requires approximation techniques for practical resolution. Despite the progress made in PAUC optimization over the last few years, most existing methods still suffer from uncontrollable approximation errors or a limited scalability when optimizing the approximate PAUC objectives. In this paper, we close the approximation gap of PAUC optimization by presenting two simple instance-wise minimax reformulations: one with an asymptotically vanishing gap, the other with the unbiasedness at the cost of more variables. Our key idea is to first establish an equivalent instance-wise problem to lower the time complexity, simplify the complicated sample selection procedure by threshold learning, and then apply different smoothing techniques. Equipped with an efficient solver, the resulting algorithms enjoy a linear per-iteration computational complexity w.r.t. the sample size and a convergence rate of $O(ε^{-1/3})$ for typical one-way and two-way PAUCs. Moreover, we provide a tight generalization bound of our minimax reformulations. The result explicitly demonstrates the impact of the TPR/FPR constraints $α$/$β$ on the generalization and exhibits a sharp order of $\tilde{O}(α^{-1}\n_+^{-1} + β^{-1}\n_-^{-1})$. Finally, extensive experiments on several benchmark datasets validate the strength of our proposed methods.

With the rapid development of electricity markets, price volatility has significantly increased, making accurate forecasting crucial for power system operations and market decisions. Traditional linear models cannot capture the complex nonlinear characteristics of electricity pricing, necessitating advanced machine learning approaches. This study compares eight machine learning models using Spanish electricity market data, integrating consumption, generation, and meteorological variables. The models evaluated include linear regression, ridge regression, decision tree, KNN, random forest, gradient boosting, SVR, and XGBoost. Results show that KNN achieves the best performance with R^2 of 0.865, MAE of 3.556, and RMSE of 5.240. To enhance interpretability, LIME analysis reveals that meteorological factors and supply-demand indicators significantly influence price fluctuations through nonlinear relationships. This work demonstrates the effectiveness of machine learning models in electricity price forecasting while improving decision transparency through interpretability analysis.