We derive explicit non-asymptotic PAC-Bayes generalization bounds for Gibbs posteriors, that is, data-dependent distributions over model parameters obtained by exponentially tilting a prior with the empirical risk. Unlike classical worst-case complexity bounds based on uniform laws of large numbers, which require explicit control of the model space in terms of metric entropy (integrals), our analysis yields posterior-averaged risk bounds that can be applied to overparameterized models and adapt to the data structure and the intrinsic model complexity. The bound involves a marginal-type integral over the parameter space, which we analyze using tools from singular learning theory to obtain explicit and practically meaningful characterizations of the posterior risk. Applications to low-rank matrix completion and ReLU neural network regression and classification show that the resulting bounds are analytically tractable and substantially tighter than classical complexity-based bounds. Our results highlight the potential of PAC-Bayes analysis for precise finite-sample generalization guarantees in modern overparameterized and singular models.

We show that the maximum expected inner product between a random vector and the standard normal vector over all couplings subject to a mutual information constraint or regularization is equivalent to a truncated integral involving the rate-distortion function, up to universal multiplicative constants. The proof is based on a lifting technique, which constructs a Gaussian process indexed by a random subset of the type class of the probability distribution involved in the information-theoretic inequality, and then applying a form of the majorizing measure theorem.

When working with real-world insurance data, practitioners often encounter challenges during the data preparation stage that can undermine the statistical validity and reliability of downstream modeling. This study illustrates that conventional data preparation procedures such as random train-test partitioning, often yield unreliable and unstable results when confronted with highly imbalanced insurance loss data. To mitigate these limitations, we propose a novel data preparation framework leveraging two recent statistical advancements: support points for representative data splitting to ensure distributional consistency across partitions, and the Chatterjee correlation coefficient for initial, non-parametric feature screening to capture feature relevance and dependence structure. We further integrate these theoretical advances into a unified, efficient framework that also incorporates missing-data handling, and embed this framework within our custom InsurAutoML pipeline. The performance of the proposed approach is evaluated using both simulated datasets and datasets often cited in the academic literature. Our findings definitively demonstrate that incorporating statistically rigorous data preparation methods not only significantly enhances model robustness and interpretability but also substantially reduces computational resource requirements across diverse insurance loss modeling tasks. This work provides a crucial methodological upgrade for achieving reliable results in high stakes insurance applications.

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Participants are not allowed to modify the training procedure.

While these advances use different algorithmic techniques, e.g., contrastive learning, diffusion, or auto-regressive modeling, they all rest on a common foundation: large datasets containing paired image-text examples.

Despite its potential benefits, applying DST to GANs presents challenges due to the adversarial nature of the training process.

Data attribution methods aim to quantify the influence of individual training samples on the prediction of artificial intelligence (AI) models.

Unlike traditional backdoor attacks that focus on specific class labels, our approach aims to induce poisoned models to predict future data as a predefined target pattern.