Cross-validation (CV) is commonly used to estimate predictive risk when independent test data are unavailable. Its validity depends on the assumption that validation tasks are sampled from the same distribution as prediction tasks encountered during deployment. In spatial prediction and other settings with structured data, this assumption is frequently violated, leading to biased estimates of deployment risk. We propose Target-Weighted CV (TWCV), an estimator of deployment risk that accounts for discrepancies between validation and deployment task distributions, thus accounting for (1) covariate shift and (2) task-difficulty shift. We characterize prediction tasks by descriptors such as covariates and spatial configuration. TWCV assigns weights to validation losses such that the weighted empirical distribution of validation tasks matches the corresponding distribution over a target domain. The weights are obtained via calibration weighting, yielding an importance-weighted estimator that targets deployment risk. Since TWCV requires adequate coverage of the deployment distribution's support, we combine it with spatially buffered resampling that diversifies the task difficulty distribution. In a simulation study, conventional as well as spatial estimators exhibit substantial bias depending on sampling, whereas buffered TWCV remains approximately unbiased across scenarios. A case study in environmental pollution mapping further confirms that discrepancies between validation and deployment task distributions can affect performance assessment, and that buffered TWCV better reflects the prediction task over the target domain. These results establish task distribution mismatch as a primary source of CV bias in spatial prediction and show that calibration weighting combined with a suitable validation task generator provides a viable approach to estimating predictive risk under dataset shift.

We derive the asymptotic risk function of regularized empirical risk minimization (ERM) estimators tuned by $n$-fold cross-validation (CV). The out-of-sample prediction loss of such estimators converges in distribution to the squared-error loss (risk function) of shrinkage estimators in the normal means model, tuned by Stein's unbiased risk estimate (SURE). This risk function provides a more fine-grained picture of predictive performance than uniform bounds on worst-case regret, which are common in learning theory: it quantifies how risk varies with the true parameter. As key intermediate steps, we show that (i) $n$-fold CV converges uniformly to SURE, and (ii) while SURE typically has multiple local minima, its global minimum is generically well separated. Well-separation ensures that uniform convergence of CV to SURE translates into convergence of the tuning parameter chosen by CV to that chosen by SURE.

Models like LASSO and ridge regression are extensively used in practice due to their interpretability, ease of use, and strong theoretical guarantees.

Cross-validation is a standard tool for obtaining a honest assessment of the performance of a prediction model. The commonly used version repeatedly splits data, trains the prediction model on the training set, evaluates the model performance on the test set, and averages the model performance across different data splits. A well-known criticism is that such cross-validation procedure does not directly estimate the performance of the particular model recommended for future use. In this paper, we propose a new method to estimate the performance of a model trained on a specific (random) training set. A naive estimator can be obtained by applying the model to a disjoint testing set. Surprisingly, cross-validation estimators computed from other random splits can be used to improve this naive estimator within a random-effects model framework. We develop two estimators -- a hierarchical Bayesian estimator and an empirical Bayes estimator -- that perform similarly to or better than both the conventional cross-validation estimator and the naive single-split estimator. Simulations and a real-data example demonstrate the superior performance of the proposed method.

When training data are fragmented across batches or federated-learned across different geographic locations, trained models manifest performance degradation. That degradation partly owes to covariate shift induced by data having been fragmented across time and space and producing dissimilar empirical training distributions. Each fragment's distribution is slightly different to a hypothetical unfragmented training distribution of covariates, and to the single validation distribution. To address this problem, we propose Fisher Information for Robust fEderated validation (\textbf{FIRE}). This method accumulates fragmentation-induced covariate shift divergences from the global training distribution via an approximate Fisher information. That term, which we prove to be a more computationally-tractable estimate, is then used as a per-fragment loss penalty, enabling scalable distribution alignment. FIRE outperforms importance weighting benchmarks by $5.1\%$ at maximum and federated learning (FL) benchmarks by up to $5.3\%$ on shifted validation sets.

Diffusion large language models (dLLMs) have recently emerged as a promising alternative to autoregressive (AR) models, offering advantages such as accelerated parallel decoding and bidirectional context modeling. However, the vanilla decoding strategy in discrete dLLMs suffers from a critical limitation: once a token is accepted, it can no longer be revised in subsequent steps. As a result, early mistakes persist across iterations, harming both intermediate predictions and final output quality. To address this issue, we propose Tolerator (Token-Level Cross-Validation Refinement), a training-free decoding strategy that leverages cross-validation among predicted tokens. Unlike existing methods that follow a single progressive unmasking procedure, Tolerator introduces a two-stage process: (i) sequence fill-up and (ii) iterative refinement by remasking and decoding a subset of tokens while treating the remaining as context. This design enables previously accepted tokens to be reconsidered and corrected when necessary, leading to more reliable diffusion decoding outputs. We evaluate Tolerator on five standard benchmarks covering language understanding, code generation, and mathematics. Experiments show that our method achieves consistent improvements over the baselines under the same computational budget. These findings suggest that decoding algorithms are crucial to realizing the full potential of diffusion large language models. Code and data are publicly available.

Breast cancer screening with mammography remains central to early detection and mortality reduction. Deep learning has shown strong potential for automating mammogram interpretation, yet limited-resolution datasets and small sample sizes continue to restrict performance. We revisit the Mini-DDSM dataset (9,684 images; 2,414 patients) and introduce a lightweight region-of-interest (ROI) augmentation strategy. During training, full images are probabilistically replaced with random ROI crops sampled from a precomputed, label-free bounding-box bank, with optional jitter to increase variability. We evaluate under strict patient-level cross-validation and report ROC-AUC, PR-AUC, and training-time efficiency metrics (throughput and GPU memory). Because ROI augmentation is training-only, inference-time cost remains unchanged. On Mini-DDSM, ROI augmentation (best: p_roi = 0.10, alpha = 0.10) yields modest average ROC-AUC gains, with performance varying across folds; PR-AUC is flat to slightly lower. These results demonstrate that simple, data-centric ROI strategies can enhance mammography classification in constrained settings without requiring additional labels or architectural modifications.

In the present work, we address (i) by extending ACV to CV schemes with dependence structure between the folds.

Careful tuning of a regularization parameter is indispensable in many machine learning tasks because it has a significant impact on generalization performances. Nevertheless, current practice of regularization parameter tuning is more of an art than a science, e.g., it is hard to tell how many grid-points would be needed in cross-validation (CV) for obtaining a solution with sufficiently small CV error. In this paper we propose a novel framework for computing a lower bound of the CV errors as a function of the regularization parameter, which we call regularization path of CV error lower bounds . The proposed framework can be used for providing a theoretical approximation guarantee on a set of solutions in the sense that how far the CV error of the current best solution could be away from best possible CV error in the entire range of the regularization parameters. Our numerical experiments demonstrate that a theoretically guaranteed choice of a regularization parameter in the above sense is possible with reasonable computational costs.