Many modern data analyses benefit from explicitly modeling dependence structure in data -- such as measurements across time or space, ordered words in a sentence, or genes in a genome. A gold standard evaluation technique is structured cross-validation (CV), which leaves out some data subset (such as data within a time interval or data in a geographic region) in each fold. But CV here can be prohibitively slow due to the need to re-run already-expensive learning algorithms many times. Previous work has shown approximate cross-validation (ACV) methods provide a fast and provably accurate alternative in the setting of empirical risk minimization. But this existing ACV work is restricted to simpler models by the assumptions that (i) data across CV folds are independent and (ii) an exact initial model fit is available. In structured data analyses, both these assumptions are often untrue.

Bayesian neural networks (BNNs) treat neural network weights as random variables, which aim to provide posterior uncertainty estimates and avoid overfitting by performing inference on the posterior weights. However, the selection of appropriate prior distributions remains a challenging task, and BNNs may suffer from catastrophic inflated variance or poor predictive performance when poor choices are made for the priors. Existing BNN designs apply different priors to weights, while the behaviours of these priors make it difficult to sufficiently shrink noisy signals or they are prone to overshrinking important signals in the weights. To alleviate this problem, we propose a novel R2D2-Net, which imposes the R^2-induced Dirichlet Decomposition (R2D2) prior to the BNN weights. The R2D2-Net can effectively shrink irrelevant coefficients towards zero, while preventing key features from over-shrinkage. To approximate the posterior distribution of weights more accurately, we further propose a variational Gibbs inference algorithm that combines the Gibbs updating procedure and gradient-based optimization. This strategy enhances stability and consistency in estimation when the variational objective involving the shrinkage parameters is non-convex. We also analyze the evidence lower bound (ELBO) and the posterior concentration rates from a theoretical perspective. Experiments on both natural and medical image classification and uncertainty estimation tasks demonstrate satisfactory performance of our method.

We present a weighted version of Leave-One-Out (LOO) cross-validation for estimating the Integrated Squared Error (ISE) when approximating an unknown function by a predictor that depends linearly on evaluations of the function over a finite collection of sites. The method relies on the construction of the best linear estimator of the squared prediction error at an arbitrary unsampled site based on squared LOO residuals, assuming that the function is a realization of a Gaussian Process (GP). A theoretical analysis of performance of the ISE estimator is presented, and robustness with respect to the choice of the GP kernel is investigated first analytically, then through numerical examples. Overall, the estimation of ISE is significantly more precise than with classical, unweighted, LOO cross validation. Application to model selection is briefly considered through examples.

Prediction-Powered Inference (PPI) is a popular strategy for combining gold-standard and possibly noisy pseudo-labels to perform statistical estimation. Prior work has shown an asymptotic "free lunch" for PPI++, an adaptive form of PPI, showing that the *asymptotic* variance of PPI++ is always less than or equal to the variance obtained from using gold-standard labels alone. Notably, this result holds *regardless of the quality of the pseudo-labels*. In this work, we demystify this result by conducting an exact finite-sample analysis of the estimation error of PPI++ on the mean estimation problem. We give a "no free lunch" result, characterizing the settings (and sample sizes) where PPI++ has provably worse estimation error than using gold-standard labels alone. Specifically, PPI++ will outperform if and only if the correlation between pseudo- and gold-standard is above a certain level that depends on the number of labeled samples ($n$). In some cases our results simplify considerably: For Gaussian data, the correlation must be at least $1/\sqrt{n - 2}$ in order to see improvement, and a similar result holds for binary labels. In experiments, we illustrate that our theoretical findings hold on real-world datasets, and give insights into trade-offs between single-sample and sample-splitting variants of PPI++.

In this paper, we analyze the classical $K$-means alternating-minimization algorithm, also known as Lloyd's algorithm (Lloyd, 1956), for a mixture of Gaussians in a data-distributed setting that incorporates local iteration steps. Assuming unlabeled data distributed across multiple machines, we propose an algorithm, LocalKMeans, that performs Lloyd's algorithm in parallel in the machines by running its iterations on local data, synchronizing only every $L$ of such local steps. We characterize the cost of these local iterations against the non-distributed setting, and show that the price paid for the local steps is a higher required signal-to-noise ratio. While local iterations were theoretically studied in the past for gradient-based learning methods, the analysis of unsupervised learning methods is more involved owing to the presence of latent variables, e.g. cluster identities, than that of an iterative gradient-based algorithm. To obtain our results, we adapt a virtual iterate method to work with a non-convex, non-smooth objective function, in conjunction with a tight statistical analysis of Lloyd steps.

Large language models (LLMs) show remarkable promise for democratizing automated reasoning by generating formal specifications. However, a fundamental tension exists: LLMs are probabilistic, while formal verification demands deterministic guarantees. This paper addresses this epistemological gap by comprehensively investigating failure modes and uncertainty quantification (UQ) in LLM-generated formal artifacts. Our systematic evaluation of five frontier LLMs reveals Satisfiability Modulo Theories (SMT) based autoformalization's domain-specific impact on accuracy (from +34.8% on logical tasks to -44.5% on factual ones), with known UQ techniques like the entropy of token probabilities failing to identify these errors. We introduce a probabilistic context-free grammar (PCFG) framework to model LLM outputs, yielding a refined uncertainty taxonomy. We find uncertainty signals are task-dependent (e.g., grammar entropy for logic, AUROC>0.93). Finally, a lightweight fusion of these signals enables selective verification, drastically reducing errors (14-100%) with minimal abstention, transforming LLM-driven formalization into a reliable engineering discipline.

In recent years, image classification, as a core task in computer vision, relies on high-quality labelled data, which restricts the wide application of deep learning models in practical scenarios. To alleviate the problem of insufficient labelled samples, semi-supervised learning has gradually become a research hotspot. In this paper, we construct a semi-supervised image classification model based on Generative Adversarial Networks (GANs), and through the introduction of the collaborative training mechanism of generators, discriminators and classifiers, we achieve the effective use of limited labelled data and a large amount of unlabelled data, improve the quality of image generation and classification accuracy, and provide an effective solution for the task of image recognition in complex environments.

Over 8,024 wildfire incidents have been documented in 2024 alone, affecting thousands of fatalities and significant damage to infrastructure and ecosystems. Wildfires in the United States have inflicted devastating losses. Wildfires are becoming more frequent and intense, which highlights how urgently efficient warning systems are needed to avoid disastrous outcomes. The goal of this study is to enhance the accuracy of wildfire detection by using Convolutional Neural Network (CNN) built on the VGG16 architecture. The D-FIRE dataset, which includes several kinds of wildfire and non-wildfire images, was employed in the study. Low-resolution images, dataset imbalance, and the necessity for real-time applicability are some of the main challenges. These problems were resolved by enriching the dataset using data augmentation techniques and optimizing the VGG16 model for binary classification. The model produced a low false negative rate, which is essential for reducing unexplored fires, despite dataset boundaries. In order to help authorities execute fast responses, this work shows that deep learning models such as VGG16 can offer a reliable, automated approach for early wildfire recognition. For the purpose of reducing the impact of wildfires, our future work will concentrate on connecting to systems with real-time surveillance networks and enlarging the dataset to cover more varied fire situations.

The growing adoption of Graph Neural Networks (GNNs) in high-stakes domains like healthcare and finance demands reliable explanations of their decision-making processes. While inherently interpretable GNN architectures like Graph Multi-linear Networks (GMT) have emerged, they remain vulnerable to generating explanations based on spurious correlations, potentially undermining trust in critical applications. We present MetaGMT, a meta-learning framework that enhances explanation fidelity through a novel bi-level optimization approach. We demonstrate that MetaGMT significantly improves both explanation quality (AUC-ROC, Precision@K) and robustness to spurious patterns, across BA-2Motifs, MUTAG, and SP-Motif benchmarks. Our approach maintains competitive classification accuracy while producing more faithful explanations (with an increase up to 8% of Explanation ROC on SP-Motif 0.5) compared to baseline methods. These advancements in interpretability could enable safer deployment of GNNs in sensitive domains by (1) facilitating model debugging through more reliable explanations, (2) supporting targeted retraining when biases are identified, and (3) enabling meaningful human oversight. By addressing the critical challenge of explanation reliability, our work contributes to building more trustworthy and actionable GNN systems for real-world applications.

Monkeypox is a viral disease characterized by distinctive skin lesions and has been reported in many countries. The recent global outbreak has emphasized the urgent need for scalable, accessible, and accurate diagnostic solutions to support public health responses. In this study, we developed ITMAINN, an intelligent, AI-driven healthcare system specifically designed to detect Monkeypox from skin lesion images using advanced deep learning techniques. Our system consists of three main components. First, we trained and evaluated several pretrained models using transfer learning on publicly available skin lesion datasets to identify the most effective models. For binary classification (Monkeypox vs. non-Monkeypox), the Vision Transformer, MobileViT, Transformer-in-Transformer, and VGG16 achieved the highest performance, each with an accuracy and F1-score of 97.8%. For multiclass classification, which contains images of patients with Monkeypox and five other classes (chickenpox, measles, hand-foot-mouth disease, cowpox, and healthy), ResNetViT and ViT Hybrid models achieved 92% accuracy, with F1 scores of 92.24% and 92.19%, respectively. The best-performing and most lightweight model, MobileViT, was deployed within the mobile application. The second component is a cross-platform smartphone application that enables users to detect Monkeypox through image analysis, track symptoms, and receive recommendations for nearby healthcare centers based on their location. The third component is a real-time monitoring dashboard designed for health authorities to support them in tracking cases, analyzing symptom trends, guiding public health interventions, and taking proactive measures. This system is fundamental in developing responsive healthcare infrastructure within smart cities. Our solution, ITMAINN, is part of revolutionizing public health management.