For training-data-based model risk prediction, $K$-fold cross-validation~(CV) is widely used to mitigate the well-known over-optimism of the empirical risk and is often regarded as reliable. However, for binary classification via empirical risk minimization, our numerical studies reveal a surprising phenomenon: $K$-fold CV may perform poorly in estimating class-specific risks, even worse than the empirical estimator. We perform a higher-order asymptotic analysis showing that $K$-fold CV may converge at a slower rate, whereas the empirical estimator exhibits a second-order asymptotic bias that explains its over-optimism. These findings motivate a novel two-step procedure for model risk prediction, termed cross-audit projection (CAP). The cross-audit step adopts the same resampling scheme as $K$-fold CV to estimate over-optimism in subsamples, while the asymptotic-theory-informed projection step adjusts for the reduced sample size in bias correction of the empirical risk. The resulting CAP estimator is first-order asymptotically equivalent to the empirical risk while achieving second-order asymptotic unbiasedness. An accompanying inference procedure is also developed. Simulation studies support theoretical advantages of CAP and demonstrate favorable finite-sample performance. An application to breast cancer detection further illustrates the proposed method.

Positive-Unlabeled (PU) learning refers to a specific weakly-supervised learning paradigm that induces a binary classifier with a few positive labeled instances and massive unlabeled instances. To handle this task, the community has proposed dozens of PU learning methods with various techniques, demonstrating strong potential. In this paper, we conduct a comprehensive study to investigate the basic characteristics of current PU learning methods. We organize them into two fundamental families of PU learning, including disambiguation-free empirical risks, which approximate the expected risk of supervised learning, and pseudo-labeling methods, which estimate pseudo-labels for unlabeled instances. First, we make an empirical analysis on disambiguation-free empirical risks such as uPU, nnPU, and DistPU, and suggest a novel risk-consistent set-aware empirical risk from the perspective of aggregate supervision. Second, we make an empirical analysis of pseudo-labeling methods to evaluate the potential of pseudo-label estimation techniques and widely applied generic tricks in PU learning. Finally, based on those empirical findings, we propose a general framework of PU learning by integrating the set-aware empirical risk with pseudo-labeling. Compared with existing PU learning methods, the proposed framework can be a practical benchmark in PU learning.

Parameter-Efficient Fine-Tuning (PEFT) is a popular class of techniques that strive to adapt large models in a scalable and resource-efficient manner. Yet, the mechanisms underlying their training performance and generalization remain underexplored. In this paper, we provide several insights into such fine-tuning through the lens of linearization. Fine-tuned models are often implicitly encouraged to remain close to the pretrained model. By making this explicit, using an ℓ2distance inductive bias in parameter space, we show that fine-tuning dynamics become equivalent to learning with the positive-definite neural tangent kernel (NTK). We specifically analyze how close the fully linear and the linearized finetuning optimizations are, based on the strength of the regularization. This allows us to be pragmatic about how good a model linearization is when fine-tuning large language models (LLMs). When linearization is a good model, our findings reveal a strong correlation between the eigenvalue spectrum of the NTK and the performance of model adaptation. Motivated by this, we give spectral perturbation bounds on the NTK induced by the choice of layers selected for fine-tuning.

Local convergence has emerged as a fundamental tool for analyzing sparse random graph models. We introduce a new notion of local convergence, color convergence, based on the Weisfeiler-Leman algorithm. Color convergence fully characterizes the class of random graphs that are well-behaved in the limit for message-passing graph neural networks. Building on this, we propose the Refined Configuration Model (RCM), a random graph model that generalizes the configuration model. The RCM is universal with respect to local convergence among locally tree-like random graph models, including Erd os-Rényi, stochastic block and configuration models. Finally, this framework enables a complete characterization of the random trees that arise as local limits of such graphs.

Positive and Unlabeled (PU) learning is a special case of binary classification with weak supervision, where only positive labeled and unlabeled data are available. Previous studies suggest several specific risk estimators of PU learning such as non-negative PU (nnPU), which are unbiased and consistent with the expected risk of supervised binary classification. In nnPU, the negative-class empirical risk is estimated by positive labeled and unlabeled data with a non-negativity constraint. However, its negative-class empirical risk estimator approaches 0, so the negative class is over-played, resulting in imbalanced error rates between positive and negative classes. To solve this problem, we suppose that the expected risks of the positive-class and negative-class should be close. Accordingly, we constrain that the negative-class empirical risk estimator is lower bounded by the positive-class empirical risk, instead of 0; and also incorporate an explicit equality constraint between them.

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