English
Related papers

Related papers: Chained Generalisation Bounds

200 papers

In this paper, we derive upper bounds on generalization errors for deep neural networks with Markov datasets. These bounds are developed based on Koltchinskii and Panchenko's approach for bounding the generalization error of combined…

Machine Learning · Statistics 2022-10-13 Lan V. Truong

Learning tasks play an increasingly prominent role in quantum information and computation. They range from fundamental problems such as state discrimination and metrology over the framework of quantum probably approximately correct (PAC)…

In this work, the probability of an event under some joint distribution is bounded by measuring it with the product of the marginals instead (which is typically easier to analyze) together with a measure of the dependence between the two…

Information Theory · Computer Science 2020-10-22 Amedeo Roberto Esposito , Michael Gastpar , Ibrahim Issa

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 propose data-dependent uniform generalization bounds by approaching the problem from a PAC-Bayesian perspective. We first apply the PAC-Bayesian framework on "random sets" in a rigorous way, where the training algorithm is assumed to…

Machine Learning · Statistics 2025-02-11 Benjamin Dupuis , Paul Viallard , George Deligiannidis , Umut Simsekli

We derive information theoretic generalization bounds for supervised learning algorithms based on a new measure of leave-one-out conditional mutual information (loo-CMI). Contrary to other CMI bounds, which are black-box bounds that do not…

Machine Learning · Computer Science 2022-07-04 Mohamad Rida Rammal , Alessandro Achille , Aditya Golatkar , Suhas Diggavi , Stefano Soatto

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 work advances the theoretical understanding of quantum learning by establishing a new family of upper bounds on the expected generalization error of quantum learning algorithms, leveraging the framework introduced by Caro et al. (2024)…

Quantum Physics · Physics 2026-04-20 Naqueeb Ahmad Warsi , Ayanava Dasgupta , Masahito Hayashi

We propose a new approach to apply the chaining technique in conjunction with information-theoretic measures to bound the generalization error of machine learning algorithms. Different from the deterministic chaining approach based on…

Information Theory · Computer Science 2022-01-31 Ruida Zhou , Chao Tian , Tie Liu

The ability of machine learning (ML) algorithms to generalize well to unseen data has been studied through the lens of information theory, by bounding the generalization error with the input-output mutual information (MI), i.e., the MI…

Machine Learning · Statistics 2024-06-07 Kimia Nadjahi , Kristjan Greenewald , Rickard Brüel Gabrielsson , Justin Solomon

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

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 derive a tight generalization bound for quantum machine learning that is applicable to a wide range of supervised tasks, data, and models. Our bound is both efficiently computable and free of big-O notation. Furthermore, we point out…

Quantum Physics · Physics 2025-10-29 Xin Wang , Rebing Wu

We establish empirical risk minimization principles for active learning by deriving a family of upper bounds on the generalization error. Aligning with empirical observations, the bounds suggest that superior query algorithms can be…

Machine Learning · Statistics 2024-09-17 Vincent Menden , Yahya Saleh , Armin Iske

Understanding the generalization abilities of modern machine learning algorithms has been a major research topic over the past decades. In recent years, the learning dynamics of Stochastic Gradient Descent (SGD) have been related to…

Machine Learning · Statistics 2023-12-04 Benjamin Dupuis , Paul Viallard

In this paper, we explore bounds on the expected risk when using deep neural networks for supervised classification from an information theoretic perspective. Firstly, we introduce model risk and fitting error, which are derived from…

Machine Learning · Computer Science 2024-10-08 Binchuan Qi

Aggregated predictors are obtained by making a set of basic predictors vote according to some weights, that is, to some probability distribution. Randomized predictors are obtained by sampling in a set of basic predictors, according to some…

Machine Learning · Statistics 2025-03-03 Pierre Alquier

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

Uncertainty quantification is essential in safety-critical settings--from autonomous driving to aviation, finance, and health--where decisions must rely on conservative bounds rather than point estimates. Predictor-level intervals (e.g.,…

Machine Learning · Computer Science 2026-05-18 Ruirui Liu , Xuejie Hou , Yiping Jiang , Hui Ren

While PAC-Bayes is now an established learning framework for light-tailed losses (\emph{e.g.}, subgaussian or subexponential), its extension to the case of heavy-tailed losses remains largely uncharted and has attracted a growing interest…

Machine Learning · Statistics 2023-04-25 Maxime Haddouche , Benjamin Guedj