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Data augmentation is one of the most widely used techniques to improve generalization in modern machine learning, often justified by its ability to promote invariance to label-irrelevant transformations. However, its theoretical role…

Machine Learning · Computer Science 2026-02-17 Abdelali Bouyahia , Frédéric LeBlanc , Mario Marchand

Distributed learning facilitates the scaling-up of data processing by distributing the computational burden over several nodes. Despite the vast interest in distributed learning, generalization performance of such approaches is not well…

Machine Learning · Statistics 2020-05-05 Martin Hellkvist , Ayça Özçelikkale , Anders Ahlén

Algorithmic stability is among the most potent techniques in generalization analysis. However, its derivation usually requires a stepsize $\eta_t = \mathcal{O}(1/t)$ under non-convex training regimes, where $t$ denotes iterations. This…

Machine Learning · Computer Science 2026-02-27 Wenquan Ma , Yang Sui , Jiaye Teng , Bohan Wang , Jing Xu , Jingqin Yang

We study the training and generalization of deep neural networks (DNNs) in the over-parameterized regime, where the network width (i.e., number of hidden nodes per layer) is much larger than the number of training data points. We show that,…

Machine Learning · Computer Science 2019-11-13 Yuan Cao , Quanquan Gu

Generalization bounds which assess the difference between the true risk and the empirical risk, have been studied extensively. However, to obtain bounds, current techniques use strict assumptions such as a uniformly bounded or a Lipschitz…

Machine Learning · Computer Science 2022-11-03 Itai Gat , Yossi Adi , Alexander Schwing , Tamir Hazan

In this work, we upper bound the generalization error of batch learning algorithms trained on samples drawn from a mixing stochastic process (i.e., a dependent data source) both in expectation and with high probability. Unlike previous…

Machine Learning · Computer Science 2025-02-20 Sagnik Chatterjee , Manuj Mukherjee , Alhad Sethi

In this article, we study rates of convergence of the generalization error of multi-class margin classifiers. In particular, we develop an upper bound theory quantifying the generalization error of various large margin classifiers. The…

Statistics Theory · Mathematics 2011-11-10 Xiaotong Shen , Lifeng Wang

The goal of machine learning is to find models that minimize prediction error on data that has not yet been seen. Its operational paradigm assumes access to a dataset $S$ and articulates a scheme for evaluating how well a given model…

Machine Learning · Computer Science 2026-04-22 Maxim Raginsky , Benjamin Recht

Established approaches to obtain generalization bounds in data-driven optimization and machine learning mostly build on solutions from empirical risk minimization (ERM), which depend crucially on the functional complexity of the hypothesis…

Optimization and Control · Mathematics 2022-10-14 Yibo Zeng , Henry Lam

To assess generalization, machine learning scientists typically either (i) bound the generalization gap and then (after training) plug in the empirical risk to obtain a bound on the true risk; or (ii) validate empirically on holdout data.…

Machine Learning · Computer Science 2021-11-09 Saurabh Garg , Sivaraman Balakrishnan , J. Zico Kolter , Zachary C. Lipton

Bounding the generalization error of a supervised learning algorithm is one of the most important problems in learning theory, and various approaches have been developed. However, existing bounds are often loose and lack of guarantees. As a…

Machine Learning · Computer Science 2021-07-30 Gholamali Aminian , Yuheng Bu , Laura Toni , Miguel R. D. Rodrigues , Gregory Wornell

Algorithm- and data-dependent generalization bounds are required to explain the generalization behavior of modern machine learning algorithms. In this context, there exists information theoretic generalization bounds that involve (various…

Machine Learning · Statistics 2023-07-07 Sarah Sachs , Tim van Erven , Liam Hodgkinson , Rajiv Khanna , Umut Simsekli

We provide sharp path-dependent generalization and excess risk guarantees for the full-batch Gradient Descent (GD) algorithm on smooth losses (possibly non-Lipschitz, possibly nonconvex). At the heart of our analysis is an upper bound on…

Machine Learning · Statistics 2023-02-13 Konstantinos E. Nikolakakis , Farzin Haddadpour , Amin Karbasi , Dionysios S. Kalogerias

We present a unifying picture of PAC-Bayesian and mutual information-based upper bounds on the generalization error of randomized learning algorithms. As we show, Tong Zhang's information exponential inequality (IEI) gives a general recipe…

Machine Learning · Computer Science 2021-10-26 Pradeep Kr. Banerjee , Guido Montúfar

One fundamental goal in any learning algorithm is to mitigate its risk for overfitting. Mathematically, this requires that the learning algorithm enjoys a small generalization risk, which is defined either in expectation or in probability.…

Machine Learning · Computer Science 2016-10-04 Ibrahim Alabdulmohsin

Supervised learning is all about the ability to generalize knowledge. Specifically, the goal of the learning is to train a classifier using training data, in such a way that it will be capable of classifying new unseen data correctly. In…

Machine Learning · Computer Science 2011-04-04 Ido Ginodi , Amir Globerson

We examine the connection between training error and generalization error for arbitrary estimating procedures, working in an overparameterized linear model under general priors in a Bayesian setup. We find determining factors inherent to…

Machine Learning · Statistics 2026-02-11 Chen Cheng , Rina Foygel Barber

Algorithm unfolding or unrolling is the technique of constructing a deep neural network (DNN) from an iterative algorithm. Unrolled DNNs often provide better interpretability and superior empirical performance over standard DNNs in signal…

Machine Learning · Statistics 2024-02-21 Carter Lyons , Raghu G. Raj , Margaret Cheney

We study the generalization error of randomized learning algorithms -- focusing on stochastic gradient descent (SGD) -- using a novel combination of PAC-Bayes and algorithmic stability. Importantly, our generalization bounds hold for all…

Machine Learning · Computer Science 2020-06-23 Ben London

The generalization bound is a crucial theoretical tool for assessing the generalizability of learning methods and there exist vast literatures on generalizability of normal learning, adversarial learning, and data poisoning. Unlike other…

Machine Learning · Computer Science 2024-06-05 Lijia Yu , Shuang Liu , Yibo Miao , Xiao-Shan Gao , Lijun Zhang