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This article offers a comprehensive treatment of polynomial functional regression, culminating in the establishment of a novel finite sample bound. This bound encompasses various aspects, including general smoothness conditions, capacity…

Numerical Analysis · Mathematics 2024-05-08 Markus Holzleitner , Sergei Pereverzyev

We establish a margin based data dependent generalization error bound for a general family of deep neural networks in terms of the depth and width, as well as the Jacobian of the networks. Through introducing a new characterization of the…

Machine Learning · Computer Science 2019-07-05 Xingguo Li , Junwei Lu , Zhaoran Wang , Jarvis Haupt , Tuo Zhao

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

We study in this paper lower bounds for the generalization error of models derived from multi-layer neural networks, in the regime where the size of the layers is commensurate with the number of samples in the training data. We show that…

Machine Learning · Statistics 2022-07-08 Inbar Seroussi , Ofer Zeitouni

It is by now well-established that modern over-parameterized models seem to elude the bias-variance tradeoff and generalize well despite overfitting noise. Many recent works attempt to analyze this phenomenon in the relatively tractable…

Machine Learning · Computer Science 2024-02-21 Daniel Barzilai , Ohad Shamir

At the heart of machine learning lies the question of generalizability of learned rules over previously unseen data. While over-parameterized models based on neural networks are now ubiquitous in machine learning applications, our…

Machine Learning · Computer Science 2020-05-04 Melikasadat Emami , Mojtaba Sahraee-Ardakan , Parthe Pandit , Sundeep Rangan , Alyson K. Fletcher

We show generalisation error bounds for deep learning with two main improvements over the state of the art. (1) Our bounds have no explicit dependence on the number of classes except for logarithmic factors. This holds even when formulating…

Machine Learning · Computer Science 2021-02-23 Antoine Ledent , Waleed Mustafa , Yunwen Lei , Marius Kloft

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

The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…

Statistics Theory · Mathematics 2023-03-17 Anna Scampicchio , Elena Arcari , Melanie N. Zeilinger

We derive generalization error bounds for the training of two-layer neural networks without assuming boundedness of the loss function, using Wasserstein distance estimates on the discrepancy between a probability distribution and its…

Machine Learning · Statistics 2026-04-09 Jiang Yu Nguwi , Nicolas Privault

Existing generalization bounds fail to explain crucial factors that drive the generalization of modern neural networks. Since such bounds often hold uniformly over all parameters, they suffer from over-parametrization and fail to account…

Machine Learning · Statistics 2023-11-14 Songyan Hou , Parnian Kassraie , Anastasis Kratsios , Andreas Krause , Jonas Rothfuss

In this paper, we propose a new framework to study the generalization property of classifier chains trained over observations associated with multiple and interdependent class labels. The results are based on large deviation inequalities…

Machine Learning · Computer Science 2018-07-27 Moura Simon , Amini Massih-Reza , Louhichi Sana , Clausel Marianne

We consider bounds on the generalization performance of the least-norm linear regressor, in the over-parameterized regime where it can interpolate the data. We describe a sense in which any generalization bound of a type that is commonly…

Machine Learning · Statistics 2021-10-19 Peter L. Bartlett , Philip M. Long

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

In this paper, we study the performance of extremum estimators from the perspective of generalization ability (GA): the ability of a model to predict outcomes in new samples from the same population. By adapting the classical concentration…

Machine Learning · Statistics 2016-09-14 Ning Xu , Jian Hong , Timothy C. G. Fisher

In this paper, we introduce various covering number bounds for linear function classes, each subject to different constraints on input and matrix norms. These bounds are contingent on the rank of each class of matrices. We then apply these…

Machine Learning · Statistics 2024-10-16 Lan V. Truong

Over-parameterization and adaptive methods have played a crucial role in the success of deep learning in the last decade. The widespread use of over-parameterization has forced us to rethink generalization by bringing forth new phenomena,…

Machine Learning · Statistics 2020-12-01 Vatsal Shah , Soumya Basu , Anastasios Kyrillidis , Sujay Sanghavi

This work provides a theoretical framework for assessing the generalization error of graph neural networks in the over-parameterized regime, where the number of parameters surpasses the quantity of data points. We explore two widely…

Machine Learning · Statistics 2024-07-02 Gholamali Aminian , Yixuan He , Gesine Reinert , Łukasz Szpruch , Samuel N. Cohen

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 2020-02-25 Yossi Adi , Yaniv Nemcovsky , Alex Schwing , Tamir Hazan

Motivated by the learned iterative soft thresholding algorithm (LISTA), we introduce a general class of neural networks suitable for sparse reconstruction from few linear measurements. By allowing a wide range of degrees of weight-sharing…

Machine Learning · Computer Science 2022-01-19 Ekkehard Schnoor , Arash Behboodi , Holger Rauhut