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Related papers: Hypothesis Set Stability and Generalization

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Recently, contrastive learning has found impressive success in advancing the state of the art in solving various machine learning tasks. However, the existing generalization analysis is very limited or even not meaningful. In particular,…

Machine Learning · Computer Science 2023-03-01 Yunwen Lei , Tianbao Yang , Yiming Ying , Ding-Xuan Zhou

Algorithmic stability is a key characteristic to ensure the generalization ability of a learning algorithm. Among different notions of stability, \emph{uniform stability} is arguably the most popular one, which yields exponential…

Machine Learning · Computer Science 2021-07-14 Zhun Deng , Hangfeng He , Weijie J. Su

Recent studies demonstrated that the adversarially robust learning under $\ell_\infty$ attack is harder to generalize to different domains than standard domain adaptation. How to transfer robustness across different domains has been a key…

Machine Learning · Computer Science 2023-02-27 Yuyang Deng , Nidham Gazagnadou , Junyuan Hong , Mehrdad Mahdavi , Lingjuan Lyu

The primary objective of learning methods is generalization. Classic uniform generalization bounds, which rely on VC-dimension or Rademacher complexity, fail to explain the significant attribute that over-parameterized models in deep…

Machine Learning · Computer Science 2025-03-07 Lijia Yu , Yibo Miao , Yifan Zhu , Xiao-Shan Gao , Lijun Zhang

Many algorithms have been recently proposed for causal machine learning. Yet, there is little to no theory on their quality, especially considering finite samples. In this work, we propose a theory based on generalization bounds that…

Machine Learning · Statistics 2024-05-16 Daniel Csillag , Claudio José Struchiner , Guilherme Tegoni Goedert

Triplet learning, i.e. learning from triplet data, has attracted much attention in computer vision tasks with an extremely large number of categories, e.g., face recognition and person re-identification. Albeit with rapid progress in…

Machine Learning · Statistics 2023-02-21 Jun Chen , Hong Chen , Xue Jiang , Bin Gu , Weifu Li , Tieliang Gong , Feng Zheng

We show that the Rademacher complexity-based framework can establish non-vacuous generalization bounds for Convolutional Neural Networks (CNNs) in the context of classifying a small set of image classes. A key technical advancement is the…

Machine Learning · Statistics 2025-03-03 Lan V. Truong

Existing Rademacher complexity bounds for neural networks rely only on norm control of the weight matrices and depend exponentially on depth via a product of the matrix norms. Lower bounds show that this exponential dependence on depth is…

Machine Learning · Computer Science 2020-04-13 Colin Wei , Tengyu Ma

In statistical learning theory, a generalization bound usually involves a complexity measure imposed by the considered theoretical framework. This limits the scope of such bounds, as other forms of capacity measures or regularizations are…

Machine Learning · Statistics 2024-02-22 Paul Viallard , Rémi Emonet , Amaury Habrard , Emilie Morvant , Valentina Zantedeschi

We study the sample complexity of learning neural networks, by providing new bounds on their Rademacher complexity assuming norm constraints on the parameter matrix of each layer. Compared to previous work, these complexity bounds have…

Machine Learning · Computer Science 2019-11-19 Noah Golowich , Alexander Rakhlin , Ohad Shamir

Deep neural networks generalize well despite being heavily overparameterized, in apparent contradiction with classical learning theory based on uniform convergence over fixed hypothesis spaces. Uniform bounds over the entire parameter space…

Machine Learning · Statistics 2026-05-15 Hubert Leroux , Jean Marcus , Julien Roger

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

In this work we consider the learning setting where, in addition to the training set, the learner receives a collection of auxiliary hypotheses originating from other tasks. We focus on a broad class of ERM-based linear algorithms that can…

Machine Learning · Computer Science 2016-10-19 Ilja Kuzborskij , Francesco Orabona

In recent times machine learning methods have made significant advances in becoming a useful tool for analyzing physical systems. A particularly active area in this theme has been "physics-informed machine learning" which focuses on using…

Machine Learning · Computer Science 2024-12-05 Pulkit Gopalani , Sayar Karmakar , Dibyakanti Kumar , Anirbit Mukherjee

In recent years, several results in the supervised learning setting suggested that classical statistical learning-theoretic measures, such as VC dimension, do not adequately explain the performance of deep learning models which prompted a…

Machine Learning · Computer Science 2021-12-09 Pascal Mattia Esser , Leena Chennuru Vankadara , Debarghya Ghoshdastidar

In this paper we introduce and analyze the learning scenario of \emph{coupled nonlinear dimensionality reduction}, which combines two major steps of machine learning pipeline: projection onto a manifold and subsequent supervised learning.…

Machine Learning · Statistics 2015-11-26 Mehryar Mohri , Afshin Rostamizadeh , Dmitry Storcheus

Generalization is one of the fundamental issues in machine learning. However, traditional techniques like uniform convergence may be unable to explain generalization under overparameterization. As alternative approaches, techniques based on…

Machine Learning · Computer Science 2022-03-22 Jiaye Teng , Jianhao Ma , Yang Yuan

We investigate the in-distribution generalization of machine learning algorithms. We depart from traditional complexity-based approaches by analyzing information-theoretic bounds that quantify the dependence between a learning algorithm and…

Machine Learning · Statistics 2024-08-27 Borja Rodríguez-Gálvez , Ragnar Thobaben , Mikael Skoglund

In this paper, we provide a new framework to obtain the generalization bounds of the learning process for domain adaptation, and then apply the derived bounds to analyze the asymptotical convergence of the learning process. Without loss of…

Machine Learning · Computer Science 2013-04-08 Chao Zhang , Lei Zhang , Jieping Ye

We investigate measures of complexity of function classes based on continuity moduli of Gaussian and Rademacher processes. For Gaussian processes, we obtain bounds on the continuity modulus on the convex hull of a function class in terms of…

Probability · Mathematics 2007-05-23 Olivier Bousquet , Vladimir Koltchinskii , Dmitry Panchenko