Objective. Type 2 diabetes mellitus (T2DM) is a highly prevalent non-communicable chronic disease that substantially reduces life expectancy. Accurate estimation of all-cause mortality risk in T2DM patients is crucial for personalizing and optimizing treatment strategies. Research Design and Methods. This study analyzed a cohort of 554 patients (aged 40-87 years) with diagnosed T2DM over a maximum follow-up period of 16.8 years, during which 202 patients (36%) died. Key survival-associated features were identified, and multiple machine learning (ML) models were trained and validated to predict all-cause mortality risk. To improve model interpretability, Shapley additive explanations (SHAP) was applied to the best-performing model. Results. The extra survival trees (EST) model, incorporating ten key features, demonstrated the best predictive performance. The model achieved a C-statistic of 0.776, with the area under the receiver operating characteristic curve (AUC) values of 0.86, 0.80, 0.841, and 0.826 for 5-, 10-, 15-, and 16.8-year all-cause mortality predictions, respectively. The SHAP approach was employed to interpret the model's individual decision-making processes. Conclusions. The developed model exhibited strong predictive performance for mortality risk assessment. Its clinically interpretable outputs enable potential bedside application, improving the identification of high-risk patients and supporting timely treatment optimization.

Physics-informed statistical learning (PISL) integrates empirical data with physical knowledge to enhance the statistical performance of estimators. While PISL methods are widely used in practice, a comprehensive theoretical understanding of how informed regularization affects statistical properties is still missing. Specifically, two fundamental questions have yet to be fully addressed: (1) what is the trade-off between considering soft penalties versus hard constraints, and (2) what is the statistical gain of incorporating physical knowledge compared to purely data-driven empirical error minimisation. In this paper, we address these questions for PISL in convex classes of functions under physical knowledge expressed as linear equations by developing appropriate complexity dependent error rates based on the small-ball method. We show that, under suitable assumptions, (1) the error rates of physics-informed estimators are comparable to those of hard constrained empirical error minimisers, differing only by constant terms, and that (2) informed penalization can effectively reduce model complexity, akin to dimensionality reduction, thereby improving learning performance. This work establishes a theoretical framework for evaluating the statistical properties of physics-informed estimators in convex classes of functions, contributing to closing the gap between statistical theory and practical PISL, with potential applications to cases not yet explored in the literature.

Generative modeling has emerged as a powerful paradigm for representation learning, but its direct applicability to challenging fields like medical imaging remains limited: mere generation, without task alignment, fails to provide a robust foundation for clinical use. We propose MAGIC-Flow, a conditional multiscale normalizing flow architecture that performs generation and classification within a single modular framework. The model is built as a hierarchy of invertible and differentiable bijections, where the Jacobian determinant factorizes across sub-transformations. We show how this ensures exact likelihood computation and stable optimization, while invertibility enables explicit visualization of sample likelihoods, providing an interpretable lens into the model's reasoning. By conditioning on class labels, MAGIC-Flow supports controllable sample synthesis and principled class-probability estimation, effectively aiding both generative and discriminative objectives. We evaluate MAGIC-Flow against top baselines using metrics for similarity, fidelity, and diversity. Across multiple datasets, it addresses generation and classification under scanner noise, and modality-specific synthesis and identification. Results show MAGIC-Flow creates realistic, diverse samples and improves classification. MAGIC-Flow is an effective strategy for generation and classification in data-limited domains, with direct benefits for privacy-preserving augmentation, robust generalization, and trustworthy medical AI.

Decomposing prediction uncertainty into its aleatoric (irreducible) and epistemic (reducible) components is critical for the development and deployment of machine learning systems. A popular, principled measure for epistemic uncertainty is the mutual information between the response variable and model parameters. However, evaluating this measure requires access to the posterior distribution of the model parameters, which is challenging to compute. In view of this, we introduce a frequentist measure of epistemic uncertainty based on the bootstrap. Our main theoretical contribution is a novel asymptotic expansion that reveals that our proposed (frequentist) measure and the (Bayesian) mutual information are asymptotically equivalent. This provides frequentist interpretations to mutual information and new computational strategies for approximating it. Moreover, we link our proposed approach to the widely-used heuristic approach of deep ensembles, giving added perspective on their practical success.

Sampling from constrained statistical distributions is a fundamental task in various fields including Bayesian statistics, computational chemistry, and statistical physics. This article considers the cases where the constrained distribution is described by an unconstrained density, as well as additional equality and/or inequality constraints, which often make the constraint set nonconvex. Existing methods for nonconvex constraint set $Σ\subset \mathbb{R}^d$ defined by equality or inequality constraints commonly rely on costly projection steps. Moreover, they cannot handle equality and inequality constraints simultaneously as each method only specialized in one case. In addition, rigorous and quantitative convergence guarantee is often lacking. In this paper, we introduce Overdamped Langevin with LAnding (OLLA), a new framework that can design overdamped Langevin dynamics accommodating both equality and inequality constraints. The proposed dynamics also deterministically corrects trajectories along the normal direction of the constraint surface, thus obviating the need for explicit projections. We show that, under suitable regularity conditions on the target density and $Σ$, OLLA converges exponentially fast in $W_2$ distance to the constrained target density $ρ_Σ(x) \propto \exp(-f(x))dσ_Σ$. Lastly, through experiments, we demonstrate the efficiency of OLLA compared to projection-based constrained Langevin algorithms and their slack variable variants, highlighting its favorable computational cost and reasonable empirical mixing.

Selecting an appropriate evaluation metric for classifiers is crucial for model comparison and parameter optimization, yet there is not consensus on a universally accepted metric that serves as a definitive standard. Moreover, there is often a misconception about the perceived need to mitigate imbalance in datasets used to train classification models. Since the final goal in classifier optimization is typically maximizing the return of investment or, equivalently, minimizing the Total Classification Cost (TCC), we define Weighted Accuracy (WA), an evaluation metric for binary classifiers with a straightforward interpretation as a weighted version of the well-known accuracy metric, coherent with the need of minimizing TCC. We clarify the conceptual framework for handling class imbalance in cost-sensitive scenarios, providing an alternative to rebalancing techniques. This framework can be applied to any metric that, like WA, can be expressed as a linear combination of example-dependent quantities and allows for comparing the results obtained in different datasets and for addressing discrepancies between the development dataset, used to train and validate the model, and the target dataset, where the model will be deployed. It also specifies in which scenarios using UCCs-unaware class rebalancing techniques or rebalancing metrics aligns with TCC minimization and when it is instead counterproductive. Finally, we propose a procedure to estimate the WA weight parameter in the absence of fully specified UCCs and demonstrate the robustness of WA by analyzing its correlation with TCC in example-dependent scenarios.

Novelty detection in large scientific datasets faces two key challenges: the noisy and high-dimensional nature of experimental data, and the necessity of making statistically robust statements about any observed outliers. While there is a wealth of literature on anomaly detection via dimensionality reduction, most methods do not produce outputs compatible with quantifiable claims of scientific discovery. In this work we directly address these challenges, presenting the first step towards a unified pipeline for novelty detection adapted for the rigorous statistical demands of science. We introduce AutoSciDACT (Automated Scientific Discovery with Anomalous Contrastive Testing), a general-purpose pipeline for detecting novelty in scientific data. AutoSciDACT begins by creating expressive low-dimensional data representations using a contrastive pre-training, leveraging the abundance of high-quality simulated data in many scientific domains alongside expertise that can guide principled data augmentation strategies. These compact embeddings then enable an extremely sensitive machine learning-based two-sample test using the New Physics Learning Machine (NPLM) framework, which identifies and statistically quantifies deviations in observed data relative to a reference distribution (null hypothesis). We perform experiments across a range of astronomical, physical, biological, image, and synthetic datasets, demonstrating strong sensitivity to small injections of anomalous data across all domains.

Probabilistic models must be well calibrated to support reliable decision-making. While calibration in single-output regression is well studied, defining and achieving multivariate calibration in multi-output regression remains considerably more challenging. The existing literature on multivariate calibration primarily focuses on diagnostic tools based on pre-rank functions, which are projections that reduce multivariate prediction-observation pairs to univariate summaries to detect specific types of miscalibration. In this work, we go beyond diagnostics and introduce a general regularization framework to enforce multivariate calibration during training for arbitrary pre-rank functions. This framework encompasses existing approaches such as highest density region calibration and copula calibration. Our method enforces calibration by penalizing deviations of the projected probability integral transforms (PITs) from the uniform distribution, and can be added as a regularization term to the loss function of any probabilistic predictor. Specifically, we propose a regularization loss that jointly enforces both marginal and multivariate pre-rank calibration. We also introduce a new PCA-based pre-rank that captures calibration along directions of maximal variance in the predictive distribution, while also enabling dimensionality reduction. Across 18 real-world multi-output regression datasets, we show that unregularized models are consistently miscalibrated, and that our methods significantly improve calibration across all pre-rank functions without sacrificing predictive accuracy.

Adversarial training has emerged as a key technique to enhance model robustness against adversarial input perturbations. Many of the existing methods rely on computationally expensive min-max problems that limit their application in practice. We propose a novel formulation of adversarial training in reproducing kernel Hilbert spaces, shifting from input to feature-space perturbations. This reformu-lation enables the exact solution of inner maximization and efficient optimization. It also provides a regularized estimator that naturally adapts to the noise level and the smoothness of the underlying function. We establish conditions under which the feature-perturbed formulation is a relaxation of the original problem and propose an efficient optimization algorithm based on iterative kernel ridge regression. We provide generalization bounds that help to understand the properties of the method. We also extend the formulation to multiple kernel learning. Empirical evaluation shows good performance in both clean and adversarial settings.

The capabilities of Large Language Models (LLMs) are routinely evaluated by other LLMs trained to predict human preferences. This framework--known as LLM-as-a-judge--is highly scalable and relatively low cost. However, it is also vulnerable to malicious exploitation, as LLM responses can be tuned to overfit the preferences of the judge. Previous work shows that the answers generated by a candidate-LLM can be edited post hoc to maximise the score assigned to them by a judge-LLM. In this study, we adopt a different approach and use the signal provided by judge-LLMs as a reward to adversarially tune models that generate text preambles designed to boost downstream performance. We find that frozen LLMs pipelined with these models attain higher LLM-evaluation scores than existing frameworks. Crucially, unlike other frameworks which intervene directly on the model's response, our method is virtually undetectable. We also demonstrate that the effectiveness of the tuned preamble generator transfers when the candidate-LLM and the judge-LLM are replaced with models that are not used during training. These findings raise important questions about the design of more reliable LLM-as-a-judge evaluation settings. They also demonstrate that human preferences can be reverse engineered effectively, by pipelining LLMs to optimise upstream preambles via reinforcement learning--an approach that could find future applications in diverse tasks and domains beyond adversarial attacks.