English
Related papers

Related papers: On Generalization Error Bounds of Noisy Gradient M…

200 papers

The generalization error of a learning algorithm refers to the discrepancy between the loss of a learning algorithm on training data and that on unseen testing data. Various information-theoretic bounds on the generalization error have been…

Information Theory · Computer Science 2025-06-24 Xuetong Wu , Jonathan H. Manton , Uwe Aickelin , Jingge Zhu

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

We consider linear prediction with a convex Lipschitz loss, or more generally, stochastic convex optimization problems of generalized linear form, i.e.~where each instantaneous loss is a scalar convex function of a linear function. We show…

Machine Learning · Computer Science 2022-11-01 Idan Amir , Roi Livni , Nathan Srebro

PAC-Bayesian is an analysis framework where the training error can be expressed as the weighted average of the hypotheses in the posterior distribution whilst incorporating the prior knowledge. In addition to being a pure generalization…

Machine Learning · Computer Science 2022-02-07 Wei Huang , Chunrui Liu , Yilan Chen , Tianyu Liu , Richard Yi Da Xu

As deep neural networks are highly expressive, it is important to find solutions with small generalization gap (the difference between the performance on the training data and unseen data). Focusing on the stochastic nature of training, we…

Machine Learning · Computer Science 2023-10-31 Rie Johnson , Tong Zhang

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

One of the main theoretical challenges in learning dynamical systems from data is providing upper bounds on the generalization error, that is, the difference between the expected prediction error and the empirical prediction error measured…

Machine Learning · Computer Science 2024-05-22 Daniel Racz , Martin Gonzalez , Mihaly Petreczky , Andras Benczur , Balint Daroczy

Algorithmic stability is a classical approach to understanding and analysis of the generalization error of learning algorithms. A notable weakness of most stability-based generalization bounds is that they hold only in expectation.…

Machine Learning · Computer Science 2019-06-25 Vitaly Feldman , Jan Vondrak

Generalization error bounds are critical to understanding the performance of machine learning models. In this work, building upon a new bound of the expected value of an arbitrary function of the population and empirical risk of a learning…

Information Theory · Computer Science 2021-05-07 Gholamali Aminian , Laura Toni , Miguel R. D. Rodrigues

Machine learning has made tremendous progress in recent years, with models matching or even surpassing humans on a series of specialized tasks. One key element behind the progress of machine learning in recent years has been the ability to…

Machine Learning · Computer Science 2020-06-30 Giorgi Nadiradze , Ilia Markov , Bapi Chatterjee , Vyacheslav Kungurtsev , Dan Alistarh

This paper uses the notion of algorithmic stability to derive novel generalization bounds for several families of transductive regression algorithms, both by using convexity and closed-form solutions. Our analysis helps compare the…

Machine Learning · Computer Science 2009-04-07 Corinna Cortes , Mehryar Mohri , Dmitry Pechyony , Ashish Rastogi

This paper takes an initial step to systematically investigate the generalization bounds of algorithms for solving nonconvex-(strongly)-concave (NC-SC/NC-C) stochastic minimax optimization measured by the stationarity of primal functions.…

Optimization and Control · Mathematics 2023-02-08 Siqi Zhang , Yifan Hu , Liang Zhang , Niao He

Stochastic Gradient Langevin Dynamics (SGLD) is a popular variant of Stochastic Gradient Descent, where properly scaled isotropic Gaussian noise is added to an unbiased estimate of the gradient at each iteration. This modest change allows…

Machine Learning · Computer Science 2017-06-06 Maxim Raginsky , Alexander Rakhlin , Matus Telgarsky

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

We derive a novel information-theoretic analysis of the generalization property of meta-learning algorithms. Concretely, our analysis proposes a generic understanding of both the conventional learning-to-learn framework and the modern…

Machine Learning · Computer Science 2021-12-13 Qi Chen , Changjian Shui , Mario Marchand

We consider two questions at the heart of machine learning; how can we predict if a minimum will generalize to the test set, and why does stochastic gradient descent find minima that generalize well? Our work responds to Zhang et al.…

Machine Learning · Computer Science 2018-02-16 Samuel L. Smith , Quoc V. Le

Most generalization bounds in learning theory are based on some measure of the complexity of the hypothesis class used, independently of any algorithm. In contrast, the notion of algorithmic stability can be used to derive tight…

Machine Learning · Computer Science 2008-11-12 Mehryar Mohri , Afshin Rostamizadeh

In this paper, the method of gaps, a technique for deriving closed-form expressions in terms of information measures for the generalization error of supervised machine learning algorithms is introduced. The method relies on the notion of…

Machine Learning · Computer Science 2026-01-01 Samir M. Perlaza , Xinying Zou

This work studies the generalization error of gradient methods. More specifically, we focus on how training steps $T$ and step-size $\eta$ might affect generalization in smooth stochastic convex optimization (SCO) problems. We first provide…

Machine Learning · Computer Science 2023-05-11 Peiyuan Zhang , Jiaye Teng , Jingzhao Zhang

The information-theoretic framework of Russo and J. Zou (2016) and Xu and Raginsky (2017) provides bounds on the generalization error of a learning algorithm in terms of the mutual information between the algorithm's output and the training…

Machine Learning · Statistics 2020-10-26 Mahdi Haghifam , Jeffrey Negrea , Ashish Khisti , Daniel M. Roy , Gintare Karolina Dziugaite