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Related papers: Information Complexity and Generalization Bounds

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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

This paper provides a general technique for lower bounding the Bayes risk of statistical estimation, applicable to arbitrary loss functions and arbitrary prior distributions. A lower bound on the Bayes risk not only serves as a lower bound…

Statistics Theory · Mathematics 2016-12-26 Xi Chen , Adityanand Guntuboyina , Yuchen Zhang

In statistical learning theory, generalization error is used to quantify the degree to which a supervised machine learning algorithm may overfit to training data. Recent work [Xu and Raginsky (2017)] has established a bound on the…

Machine Learning · Computer Science 2018-01-16 Ankit Pensia , Varun Jog , Po-Ling Loh

Generalization error (also known as the out-of-sample error) measures how well the hypothesis learned from training data generalizes to previously unseen data. Proving tight generalization error bounds is a central question in statistical…

Machine Learning · Computer Science 2020-03-03 Jian Li , Xuanyuan Luo , Mingda Qiao

Understanding the generalization behavior of deep neural networks remains a fundamental challenge in modern statistical learning theory. Among existing approaches, PAC-Bayesian norm-based bounds have demonstrated particular promise due to…

Machine Learning · Statistics 2026-01-14 Xinping Yi , Gaojie Jin , Xiaowei Huang , Shi Jin

We present a framework to derive bounds on the test loss of randomized learning algorithms for the case of bounded loss functions. Drawing from Steinke & Zakynthinou (2020), this framework leads to bounds that depend on the conditional…

Machine Learning · Computer Science 2021-03-11 Fredrik Hellström , Giuseppe Durisi

The Probably Approximately Correct (PAC) Bayes framework (McAllester, 1999) can incorporate knowledge about the learning algorithm and (data) distribution through the use of distribution-dependent priors, yielding tighter generalization…

Machine Learning · Computer Science 2019-04-22 Gintare Karolina Dziugaite , Daniel M. Roy

We study the generalization error of stochastic learning algorithms from an information-theoretic perspective, with a particular emphasis on deriving sharper bounds for differentially private algorithms. It is well known that the…

Information Theory · Computer Science 2026-04-20 Yanxiao Liu , Chun Hei Michael Shiu , Lele Wang , Deniz Gündüz

Data-driven algorithms can adapt their internal structure or parameters to inputs from unknown application-specific distributions, by learning from a training sample of inputs. Several recent works have applied this approach to problems in…

Machine Learning · Computer Science 2022-06-17 Peter Bartlett , Piotr Indyk , Tal Wagner

Standard Bayesian learning is known to have suboptimal generalization capabilities under misspecification and in the presence of outliers. PAC-Bayes theory demonstrates that the free energy criterion minimized by Bayesian learning is a…

Machine Learning · Computer Science 2023-04-25 Matteo Zecchin , Sangwoo Park , Osvaldo Simeone , Marios Kountouris , David Gesbert

The PAC-Bayesian framework has significantly advanced the understanding of statistical learning, particularly for majority voting methods. Despite its successes, its application to multi-view learning -- a setting with multiple…

Machine Learning · Computer Science 2025-10-15 Mehdi Hennequin , Abdelkrim Zitouni , Khalid Benabdeslem , Haytham Elghazel , Yacine Gaci

We present here a PAC-Bayesian point of view on adaptive supervised classification. Using convex analysis, we show how to get local measures of the complexity of the classification model involving the relative entropy of posterior…

Statistics Theory · Mathematics 2007-06-13 Olivier Catoni

In this work, we propose a PAC-Bayes bound for the generalization risk of the Gibbs classifier in the multi-class classification framework. The novelty of our work is the critical use of the confusion matrix of a classifier as an error…

Machine Learning · Statistics 2013-10-23 Emilie Morvant , Sokol Koço , Liva Ralaivola

We derive PAC-Bayesian learning guarantees for heavy-tailed losses, and obtain a novel optimal Gibbs posterior which enjoys finite-sample excess risk bounds at logarithmic confidence. Our core technique itself makes use of PAC-Bayesian…

Machine Learning · Statistics 2019-12-19 Matthew J. Holland

Transfer learning has received a lot of attention in the machine learning community over the last years, and several effective algorithms have been developed. However, relatively little is known about their theoretical properties,…

Machine Learning · Statistics 2014-05-13 Anastasia Pentina , Christoph H. Lampert

Deep neural networks (DNNs) exhibit an exceptional capacity for generalization in practical applications. This work aims to capture the effect and benefits of depth for supervised learning via information-theoretic generalization bounds. We…

Machine Learning · Computer Science 2025-05-09 Haiyun He , Ziv Goldfeld

We present a new framework for deriving bounds on the generalization bound of statistical learning algorithms from the perspective of online learning. Specifically, we construct an online learning game called the "generalization game",…

Machine Learning · Statistics 2024-10-18 Gábor Lugosi , Gergely Neu

We provide a new information-theoretic generalization error bound that is exactly tight (i.e., matching even the constant) for the canonical quadratic Gaussian (location) problem. Most existing bounds are order-wise loose in this setting,…

Information Theory · Computer Science 2023-11-14 Ruida Zhou , Chao Tian , Tie Liu

We consider information-theoretic bounds on expected generalization error for statistical learning problems in a networked setting. In this setting, there are $K$ nodes, each with its own independent dataset, and the models from each node…

Information Theory · Computer Science 2024-01-17 L. P. Barnes , Alex Dytso , H. V. Poor

The sample complexity of estimating or maximising an unknown function in a reproducing kernel Hilbert space is known to be linked to both the effective dimension and the information gain associated with the kernel. While the information…

Machine Learning · Statistics 2026-01-16 Hamish Flynn