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We study grokking, the onset of generalization long after overfitting, in a classical ridge regression setting. We prove end-to-end grokking results for learning over-parameterized linear regression models using gradient descent with weight…

Machine Learning · Computer Science 2026-02-09 Mingyue Xu , Gal Vardi , Itay Safran

Meta-learning involves training models on a variety of training tasks in a way that enables them to generalize well on new, unseen test tasks. In this work, we consider meta-learning within the framework of high-dimensional multivariate…

Statistics Theory · Mathematics 2024-04-01 Yanhao Jin , Krishnakumar Balasubramanian , Debashis Paul

State-of-the-art link prediction (LP) models demonstrate impressive benchmark results. However, popular benchmark datasets often assume that training, validation, and testing samples are representative of the overall dataset distribution.…

Machine Learning · Computer Science 2025-07-17 Jay Revolinsky , Harry Shomer , Jiliang Tang

The linear regression model cannot be fitted to high-dimensional data, as the high-dimensionality brings about empirical non-identifiability. Penalized regression overcomes this non-identifiability by augmentation of the loss function by a…

Methodology · Statistics 2023-06-29 Wessel N. van Wieringen

Distributionally robust policy learning aims to find a policy that performs well under the worst-case distributional shift, and yet most existing methods for robust policy learning consider the worst-case joint distribution of the covariate…

Machine Learning · Computer Science 2025-06-03 Jingyuan Wang , Zhimei Ren , Ruohan Zhan , Zhengyuan Zhou

This paper addresses the covariate shift problem in the context of nonparametric regression within reproducing kernel Hilbert spaces (RKHSs). Covariate shift arises in supervised learning when the input distributions of the training and…

Machine Learning · Statistics 2025-05-21 Andrea Della Vecchia , Arnaud Mavakala Watusadisi , Ernesto De Vito , Lorenzo Rosasco

In this paper, we propose Test-Time Training, a general approach for improving the performance of predictive models when training and test data come from different distributions. We turn a single unlabeled test sample into a self-supervised…

Machine Learning · Computer Science 2020-07-03 Yu Sun , Xiaolong Wang , Zhuang Liu , John Miller , Alexei A. Efros , Moritz Hardt

Deep neural networks often produce overconfident predictions, undermining their reliability in safety-critical applications. This miscalibration is further exacerbated under distribution shift, where test data deviates from the training…

Computer Vision and Pattern Recognition · Computer Science 2025-08-28 Yilin Zhang , Cai Xu , You Wu , Ziyu Guan , Wei Zhao

Most machine learning models are static, but the world is dynamic, and increasing online deployment of learned models gives increasing urgency to the development of efficient and effective mechanisms to address learning in the context of…

Machine Learning · Computer Science 2016-11-16 Geoffrey I. Webb , Roy Hyde , Hong Cao , Hai Long Nguyen , Francois Petitjean

Learning with identical train and test distributions has been extensively investigated both practically and theoretically. Much remains to be understood, however, in statistical learning under distribution shifts. This paper focuses on a…

Machine Learning · Computer Science 2024-11-01 Omar Montasser , Han Shao , Emmanuel Abbe

This note continues study of exchangeability martingales, i.e., processes that are martingales under any exchangeable distribution for the observations. Such processes can be used for detecting violations of the IID assumption, which is…

Machine Learning · Computer Science 2020-12-29 Vladimir Vovk

In this work, we investigate the behavior of ridge regression in an overparameterized binary classification task. We assume examples are drawn from (anisotropic) class-conditional cluster distributions with opposing means and we allow for…

Machine Learning · Statistics 2025-03-12 Alexander Tsigler , Luiz F. O. Chamon , Spencer Frei , Peter L. Bartlett

We study the behavior of optimal ridge regularization and optimal ridge risk for out-of-distribution prediction, where the test distribution deviates arbitrarily from the train distribution. We establish general conditions that determine…

Statistics Theory · Mathematics 2024-04-02 Pratik Patil , Jin-Hong Du , Ryan J. Tibshirani

In real-life applications, machine learning models often face scenarios where there is a change in data distribution between training and test domains. When the aim is to make predictions on distributions different from those seen at…

Machine Learning · Computer Science 2021-11-04 Lucas Mansilla , Rodrigo Echeveste , Diego H. Milone , Enzo Ferrante

Many existing approaches for generating predictions in settings with distribution shift model distribution shifts as adversarial or low-rank in suitable representations. In various real-world settings, however, we might expect shifts to…

Machine Learning · Statistics 2023-10-31 Kirk Bansak , Elisabeth Paulson , Dominik Rothenhäusler

Safe Reinforcement Learning (RL) algorithms are typically evaluated under fixed training conditions. We investigate whether training-time safety guarantees transfer to deployment under distribution shift, using diabetes management as a…

Machine Learning · Computer Science 2026-05-26 Minjae Kwon , Josephine Lamp , Lu Feng

Information from related source studies can often enhance the findings of a target study. However, the distribution shift between target and source studies can severely impact the efficiency of knowledge transfer. In the high-dimensional…

Methodology · Statistics 2025-11-26 Ruiqi Bai , Yijiao Zhang , Hanbo Yang , Zhongyi Zhu

Dealing with distribution shifts is one of the central challenges for modern machine learning. One fundamental situation is the covariate shift, where the input distributions of data change from training to testing stages while the…

Machine Learning · Computer Science 2024-05-28 Yu-Jie Zhang , Zhen-Yu Zhang , Peng Zhao , Masashi Sugiyama

Transformers serve as the foundational architecture for many successful large-scale models, demonstrating the ability to overfit the training data while maintaining strong generalization on unseen data, a phenomenon known as benign…

Machine Learning · Computer Science 2025-02-19 Yingying Zhang , Zhenyu Wu , Jian Li , Yong Liu

Machine learning models often degrade when deployed on data distributions different from their training data. Challenging conventional validation paradigms, we demonstrate that higher in-distribution (ID) bias can lead to better…

Machine Learning · Computer Science 2025-06-03 Ruixuan Chen , Wentao Li , Jiahui Xiao , Yuchen Li , Yimin Tang , Xiaonan Wang