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We propose new bounds on the error of learning algorithms in terms of a data-dependent notion of complexity. The estimates we establish give optimal rates and are based on a local and empirical version of Rademacher averages, in the sense…

Statistics Theory · Mathematics 2007-06-13 Peter L. Bartlett , Olivier Bousquet , Shahar Mendelson

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 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

We derive an upper bound on the local Rademacher complexity of $\ell_p$-norm multiple kernel learning, which yields a tighter excess risk bound than global approaches. Previous local approaches aimed at analyzed the case $p=1$ only while…

Machine Learning · Statistics 2011-03-07 Marius Kloft , Gilles Blanchard

This paper provides norm-based generalization bounds for the Transformer architecture that do not depend on the input sequence length. We employ a covering number based approach to prove our bounds. We use three novel covering number bounds…

Machine Learning · Statistics 2023-10-23 Jacob Trauger , Ambuj Tewari

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

One of the main open problems in the theory of multi-category margin classification is the form of the optimal dependency of a guaranteed risk on the number C of categories, the sample size m and the margin parameter gamma. From a practical…

Statistics Theory · Mathematics 2018-12-04 Khadija Musayeva , Fabien Lauer , Yann Guermeur

We present a novel notion of complexity that interpolates between and generalizes some classic existing complexity notions in learning theory: for estimators like empirical risk minimization (ERM) with arbitrary bounded losses, it is upper…

Machine Learning · Computer Science 2017-10-24 Peter D. Grünwald , Nishant A. Mehta

In this paper we introduce an alternative localization approach for binary classification that leads to a novel complexity measure: fixed points of the local empirical entropy. We show that this complexity measure gives a tight control over…

Statistics Theory · Mathematics 2017-12-19 Nikita Zhivotovskiy , Steve Hanneke

Understanding and certifying the generalization performance of machine learning algorithms -- i.e. obtaining theoretical estimates of the test error from the training error -- is a central theme of statistical learning theory. Among the…

Machine Learning · Computer Science 2026-05-26 Sho Sonoda , Kazumi Kasaura , Yuma Mizuno , Kei Tsukamoto , Naoto Onda

We study the excess capacity of deep networks in the context of supervised classification. That is, given a capacity measure of the underlying hypothesis class - in our case, empirical Rademacher complexity - to what extent can we (a…

Machine Learning · Computer Science 2023-01-20 Florian Graf , Sebastian Zeng , Bastian Rieck , Marc Niethammer , Roland Kwitt

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

This paper proposes a simple approach to derive efficient error bounds for learning multiple components with sparsity-inducing regularization. We show that for such regularization schemes, known decompositions of the Rademacher complexity…

Machine Learning · Statistics 2020-01-24 Fabien Lauer

This paper studies generalization error bounds for Transformer models. Based on the offset Rademacher complexity, we derive sharper generalization bounds for different Transformer architectures, including single-layer single-head,…

Machine Learning · Computer Science 2026-03-24 Yawen Li , Tao Hu , Zhouhui Lian , Wan Tian , Yijie Peng , Huiming Zhang , Zhongyi Li

Linear predictors form a rich class of hypotheses used in a variety of learning algorithms. We present a tight analysis of the empirical Rademacher complexity of the family of linear hypothesis classes with weight vectors bounded in…

Machine Learning · Computer Science 2020-07-23 Pranjal Awasthi , Natalie Frank , Mehryar Mohri

We construct data dependent bounds on the risk in function learning problems. The bounds are based on the local norms of the Rademacher process indexed by the underlying function class and they do not require prior knowledge about the…

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

We develop a technique for deriving data-dependent error bounds for transductive learning algorithms based on transductive Rademacher complexity. Our technique is based on a novel general error bound for transduction in terms of…

Machine Learning · Computer Science 2014-01-16 Ran El-Yaniv , Dmitry Pechyony

Following the seminal approach by Talagrand, the concept of Rademacher complexity for independent sequences of random variables is extended to Markov chains. The proposed notion of "block Rademacher complexity" (of a class of functions)…

Statistics Theory · Mathematics 2018-07-09 Patrice Bertail , François Portier

We present a series of new and more favorable margin-based learning guarantees that depend on the empirical margin loss of a predictor. We give two types of learning bounds, both distribution-dependent and valid for general families, in…

Machine Learning · Computer Science 2020-10-30 Corinna Cortes , Mehryar Mohri , Ananda Theertha Suresh

We propose a way to bound the generalisation errors of several classes of quantum reservoirs using the Rademacher complexity. We give specific, parameter-dependent bounds for two particular quantum reservoir classes. We analyse how the…

Machine Learning · Computer Science 2025-01-16 Naomi Mona Chmielewski , Nina Amini , Joseph Mikael
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