This study develops a hierarchical Bayesian framework that integrates expert domain knowledge to quantify player-specific effects in expected goals (xG) estimation, addressing a limitation of standard models that treat all players as identical finishers. Using 9,970 shots from StatsBomb's 2015-16 data and Football Manager 2017 ratings, we combine Bayesian logistic regression with informed priors to stabilise player-level estimates, especially for players with few shots. The hierarchical model reduces posterior uncertainty relative to weak priors and achieves strong external validity: hierarchical and baseline predictions correlate at R2 = 0.75, while an XGBoost benchmark validated against StatsBomb xG reaches R2 = 0.833. The model uncovers interpretable specialisation profiles, including one-on-one finishing (Aguero, Suarez, Belotti, Immobile, Martial), long-range shooting (Pogba), and first-touch execution (Insigne, Salah, Gameiro). It also identifies latent ability in underperforming players such as Immobile and Belotti. The framework supports counterfactual "what-if" analysis by reallocating shots between players under identical contexts. Case studies show that Sansone would generate +2.2 xG from Berardi's chances, driven largely by high-pressure situations, while Vardy-Giroud substitutions reveal strong asymmetry: replacing Vardy with Giroud results in a large decline (about -7 xG), whereas the reverse substitution has only a small effect (about -1 xG). This work provides an uncertainty-aware tool for player evaluation, recruitment, and tactical planning, and offers a general approach for domains where individual skill and contextual factors jointly shape performance.

Accurately dating historical texts is essential for organizing and interpreting cultural heritage collections. This article addresses temporal text classification using interpretable, feature-engineered tree-based machine learning models. We integrate five feature categories - compression-based, lexical structure, readability, neologism detection, and distance features - to predict the temporal origin of English texts spanning five centuries. Comparative analysis shows that these feature domains provide complementary temporal signals, with combined models outperforming any individual feature set. On a large-scale corpus, we achieve 76.7% accuracy for century-scale prediction and 26.1% for decade-scale classification, substantially above random baselines (20% and 2.3%). Under relaxed temporal precision, performance increases to 96.0% top-2 accuracy for centuries and 85.8% top-10 accuracy for decades. The final model exhibits strong ranking capabilities with AUCROC up to 94.8% and AUPRC up to 83.3%, and maintains controlled errors with mean absolute deviations of 27 years and 30 years, respectively. For authentication-style tasks, binary models around key thresholds (e.g., 1850-1900) reach 85-98% accuracy. Feature importance analysis identifies distance features and lexical structure as most informative, with compression-based features providing complementary signals. SHAP explainability reveals systematic linguistic evolution patterns, with the 19th century emerging as a pivot point across feature domains. Cross-dataset evaluation on Project Gutenberg highlights domain adaptation challenges, with accuracy dropping by 26.4 percentage points, yet the computational efficiency and interpretability of tree-based models still offer a scalable, explainable alternative to neural architectures.

Abstract-- We study automated intrusion prediction in an IT system using statistical learning methods. The focus is on developing online attack predictors that detect attacks in real time and identify the current stage of the attack. While such predictors have been proposed in the recent literature, these works typically rely on constructing a monolithic predictor tailored to a specific attack type and scenario. Given that hundreds of attack types are cataloged in the MITRE framework, training a separate monolithic predictor for each of them is infeasible. In this paper, we propose a modular framework for rapidly assembling online attack predictors from reusable components. Using public datasets for training and evaluation, we provide many examples of modular predictors and show how an effective predictor can be dynamically assembled during training from a network of modular components. Traditional intrusion detection systems (IDS), such as Snort [1] or Suricata [2], rely on rule-based configurations that are manually crafted and maintained by domain experts. The growing complexity and rapid evolution of IT systems make the maintenance of these rules increasingly challenging and time-consuming. As a response, research efforts into automated cyberdefence have started, based on the idea that attack patterns can be dynamically learned. The rules are no longer defined by humans, but automatically inferred from observing systems under attack. Over the last decade, various approaches have been proposed for automated cyberdefence, most of them based on statistical learning, e.g., [3], [4], [5], [6]. We follow this direction in the paper. We are specifically interested in predicting the stage of an ongoing attack in real time, based on current and earlier observations of an IT system.

Recent advances in Neural Radiance Fields (NeRFs) and 3D Gaussian Splatting (3DGS) have achieved considerable performance in RGB scene reconstruction. However, multi-modal rendering that incorporates thermal infrared imagery remains largely underexplored. Existing approaches tend to neglect distinctive thermal characteristics, such as heat conduction and the Lambertian property. In this study, we introduce MrGS, a multi-modal radiance field based on 3DGS that simultaneously reconstructs both RGB and thermal 3D scenes. Specifically, MrGS derives RGB- and thermal-related information from a single appearance feature through orthogonal feature extraction and employs view-dependent or view-independent embedding strategies depending on the degree of Lambertian reflectance exhibited by each modality. Furthermore, we leverage two physics-based principles to effectively model thermal-domain phenomena. First, we integrate Fourier's law of heat conduction prior to alpha blending to model intensity interpolation caused by thermal conduction between neighboring Gaussians. Second, we apply the Stefan-Boltzmann law and the inverse-square law to formulate a depth-aware thermal radiation map that imposes additional geometric constraints on thermal rendering. Experimental results demonstrate that the proposed MrGS achieves high-fidelity RGB-T scene reconstruction while reducing the number of Gaussians.

In open-world scenarios, Generalized Category Discovery (GCD) requires identifying both known and novel categories within unlabeled data. However, existing methods often suffer from prototype confusion caused by shortcut learning, which undermines generalization and leads to forgetting of known classes. We propose ClearGCD, a framework designed to mitigate reliance on non-semantic cues through two complementary mechanisms. First, Semantic View Alignment (SVA) generates strong augmentations via cross-class patch replacement and enforces semantic consistency using weak augmentations. Second, Shortcut Suppression Regularization (SSR) maintains an adaptive prototype bank that aligns known classes while encouraging separation of potential novel ones. ClearGCD can be seamlessly integrated into parametric GCD approaches and consistently outperforms state-of-the-art methods across multiple benchmarks.

As cities around the world aim to improve walkability and safety, understanding the irregular and unpredictable nature of pedestrian behavior has become increasingly important. This study introduces a data-driven framework for modeling chaotic pedestrian movement using empirically observed trajectory data and supervised learning. Videos were recorded during both daytime and nighttime conditions to capture pedestrian dynamics under varying ambient and traffic contexts. Pedestrian trajectories were extracted through computer vision techniques, and behavioral chaos was quantified using four chaos metrics: Approximate Entropy and Lyapunov Exponent, each computed for both velocity and direction change. A Principal Component Analysis (PCA) was then applied to consolidate these indicators into a unified chaos score. A comprehensive set of individual, group-level, and contextual traffic features was engineered and used to train Random Forest and CatBoost regression models. CatBoost models consistently achieved superior performance. The best daytime PCA-based CatBoost model reached an R^2 of 0.8319, while the nighttime PCA-based CatBoost model attained an R^2 of 0.8574. SHAP analysis highlighted that features such as distance travel, movement duration, and speed variability were robust contributors to chaotic behavior. The proposed framework enables practitioners to quantify and anticipate behavioral instability in real-world settings. Planners and engineers can use chaos scores to identify high-risk pedestrian zones, apprise infrastructure improvements, and calibrate realistic microsimulation models. The approach also supports adaptive risk assessment in automated vehicle systems by capturing short-term motion unpredictability grounded in observable, interpretable features.

To understand how neural systems process information, it is often essential to compare one circuit with another, one brain with another, or data with a model. Traditional similarity measures ignore the dynamical processes underlying neural representations. Dynamical similarity methods offer a framework to compare the temporal structure of dynamical systems by embedding their (possibly) nonlinear dynamics into a globally linear space and there computing conjugacy metrics. However, identifying the best embedding and computing these metrics can be computationally slow. Here we introduce fast Dynamical Similarity Analysis (fastDSA), which is computationally far more efficient than previous methods while maintaining their accuracy and robustness. FastDSA introduces two key components that boost efficiency: (1) automatic selection of the effective model order of the Hankel (delay) embedding from the data via a data-driven singular-value threshold that identifies the informative subspace and discards noise to lower computational cost without sacrificing signal, and (2) a novel optimization procedure and objective, which replaces the slow exact orthogonality constraint in finding a minimal distance between dynamics matrices with a lightweight process to keep the search close to the space of orthogonal transformations. We demonstrate that fastDSA is at least an order of magnitude faster than the previous methods. Furthermore, we demonstrate that fastDSA has the properties of its ancestor, including its invariances and sensitivities to system dynamics. FastDSA, therefore, provides a computationally efficient and accurate method for dynamical similarity analysis.

Weakly supervised learning has emerged as a practical alternative to fully supervised learning when complete and accurate labels are costly or infeasible to acquire. However, many existing methods are tailored to specific supervision patterns -- such as positive-unlabeled (PU), unlabeled-unlabeled (UU), complementary-label (CLL), partial-label (PLL), or similarity-unlabeled annotations -- and rely on post-hoc corrections to mitigate instability induced by indirect supervision. We propose a principled, unified framework that bypasses such post-hoc adjustments by directly formulating a stable surrogate risk grounded in the structure of weakly supervised data. The formulation naturally subsumes diverse settings -- including PU, UU, CLL, PLL, multi-class unlabeled, and tuple-based learning -- under a single optimization objective. We further establish a non-asymptotic generalization bound via Rademacher complexity that clarifies how supervision structure, model capacity, and sample size jointly govern performance. Beyond this, we analyze the effect of class-prior misspecification on the bound, deriving explicit terms that quantify its impact, and we study identifiability, giving sufficient conditions -- most notably via supervision stratification across groups -- under which the target risk is recoverable. Extensive experiments show consistent gains across class priors, dataset scales, and class counts -- without heuristic stabilization -- while exhibiting robustness to overfitting.

Many machine learning models perform well when making predictions within the training data range, but often struggle when required to extrapolate beyond it. Symbolic regression (SR) using genetic programming (GP) can generate flexible models but is prone to unreliable behaviour in extrapolation. This paper investigates whether adding synthetic data can help improve performance in such cases. We apply Kernel Density Estimation (KDE) to identify regions in the input space where the training data is sparse. Synthetic data is then generated in those regions using a knowledge distillation approach: a teacher model generates predictions on new input points, which are then used to train a student model. We evaluate this method across six benchmark datasets, using neural networks (NN), random forests (RF), and GP both as teacher models (to generate synthetic data) and as student models (trained on the augmented data). Results show that GP models can often improve when trained on synthetic data, especially in extrapolation areas. However, the improvement depends on the dataset and teacher model used. The most important improvements are observed when synthetic data from GPe is used to train GPp in extrapolation regions. Changes in interpolation areas show only slight changes. We also observe heterogeneous errors, where model performance varies across different regions of the input space. Overall, this approach offers a practical solution for better extrapolation. Note: An earlier version of this work appeared in the GECCO 2025 Workshop on Symbolic Regression. This arXiv version corrects several parts of the original submission.

Vision-Language Action (VLAs) models promise to extend the remarkable success of vision-language models (VLMs) to robotics. Yet, unlike VLMs in the vision-language domain, VLAs for robotics require finetuning to contend with varying physical factors like robot embodiment, environment characteristics, and spatial relationships of each task. Existing fine-tuning methods lack specificity, adapting the same set of parameters regardless of a task's visual, linguistic, and physical characteristics. Inspired by functional specificity in neuroscience, we hypothesize that it is more effective to finetune sparse model representations specific to a given task. In this work, we introduce Robotic Steering, a finetuning approach grounded in mechanistic interpretability that leverages few-shot demonstrations to identify and selectively finetune task-specific attention heads aligned with the physical, visual, and linguistic requirements of robotic tasks. Through comprehensive on-robot evaluations with a Franka Emika robot arm, we demonstrate that Robotic Steering outperforms LoRA while achieving superior robustness under task variation, reduced computational cost, and enhanced interpretability for adapting VLAs to diverse robotic tasks.