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Concentration inequalities are indispensable tools for studying the generalization capacity of learning models. Hoeffding's and McDiarmid's inequalities are commonly used, giving bounds independent of the data distribution. Although this…

Machine Learning · Statistics 2017-02-21 Xinxing Wu , Junping Zhang

We obtain a tight distribution-specific characterization of the sample complexity of large-margin classification with L2 regularization: We introduce the margin-adapted dimension, which is a simple function of the second order statistics of…

Machine Learning · Statistics 2013-09-19 Sivan Sabato , Nathan Srebro , Naftali Tishby

By transferring knowledge learned from seen/previous tasks, meta learning aims to generalize well to unseen/future tasks. Existing meta-learning approaches have shown promising empirical performance on various multiclass classification…

Machine Learning · Computer Science 2020-12-04 Jiechao Guan , Zhiwu Lu , Tao Xiang , Timothy Hospedales

We present novel bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These are nearly optimal in various precise senses, including a kind of instance-optimality. Our data-dependent convergence guarantees…

Statistics Theory · Mathematics 2024-02-14 Aryeh Kontorovich , Amichai Painsky

We prove the first margin-based generalization bound for voting classifiers, that is asymptotically tight in the tradeoff between the size of the hypothesis set, the margin, the fraction of training points with the given margin, the number…

Machine Learning · Computer Science 2025-11-26 Kasper Green Larsen , Natascha Schalburg

We study classification problems using binary estimators where the decision boundary is described by horizon functions and where the data distribution satisfies a geometric margin condition. A key novelty of our work is the derivation of…

Machine Learning · Statistics 2026-03-16 Jonathan García , Philipp Petersen

We study two-layer belief networks of binary random variables in which the conditional probabilities Pr[childlparents] depend monotonically on weighted sums of the parents. In large networks where exact probabilistic inference is…

Machine Learning · Computer Science 2013-02-01 Michael Kearns , Lawrence Saul

In this paper, we derive generic bounds on the maximum deviations in prediction errors for sequential prediction via an information-theoretic approach. The fundamental bounds are shown to depend only on the conditional entropy of the data…

Machine Learning · Computer Science 2021-05-12 Song Fang , Quanyan Zhu

In this article, we study rates of convergence of the generalization error of multi-class margin classifiers. In particular, we develop an upper bound theory quantifying the generalization error of various large margin classifiers. The…

Statistics Theory · Mathematics 2011-11-10 Xiaotong Shen , Lifeng Wang

This article studies the achievable guarantees on the error rates of certain learning algorithms, with particular focus on refining logarithmic factors. Many of the results are based on a general technique for obtaining bounds on the error…

Machine Learning · Computer Science 2016-09-13 Steve Hanneke

We derive bounds for a notion of adversarial risk, designed to characterize the robustness of linear and neural network classifiers to adversarial perturbations. Specifically, we introduce a new class of function transformations with the…

Machine Learning · Statistics 2019-01-03 Justin Khim , Po-Ling Loh

In this paper, we correct an upper bound, presented in~\cite{hs-11}, on the generalisation error of classifiers learned through multiple kernel learning. The bound in~\cite{hs-11} uses Rademacher complexity and has an\emph{additive}…

Machine Learning · Computer Science 2014-05-13 Zakria Hussain , John Shawe-Taylor , Mario Marchand

We present a study of generalization for data-dependent hypothesis sets. We give a general learning guarantee for data-dependent hypothesis sets based on a notion of transductive Rademacher complexity. Our main result is a generalization…

Machine Learning · Computer Science 2020-10-06 Dylan J. Foster , Spencer Greenberg , Satyen Kale , Haipeng Luo , Mehryar Mohri , Karthik Sridharan

The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…

Statistics Theory · Mathematics 2022-11-15 Loris Michel , Jeffrey Näf , Nicolai Meinshausen

Understanding the generalization of deep neural networks is one of the most important tasks in deep learning. Although much progress has been made, theoretical error bounds still often behave disparately from empirical observations. In this…

Machine Learning · Computer Science 2021-11-09 Ching-Yao Chuang , Youssef Mroueh , Kristjan Greenewald , Antonio Torralba , Stefanie Jegelka

We study the behavior of error bounds for multiclass classification under suitable margin conditions. For a wide variety of methods we prove that the classification error under a hard-margin condition decreases exponentially fast without…

Machine Learning · Statistics 2022-02-04 Stefano Vigogna , Giacomo Meanti , Ernesto De Vito , Lorenzo Rosasco

In this paper, we provide a new framework to obtain the generalization bounds of the learning process for domain adaptation, and then apply the derived bounds to analyze the asymptotical convergence of the learning process. Without loss of…

Machine Learning · Computer Science 2013-04-08 Chao Zhang , Lei Zhang , Jieping Ye

We present a formulation of deep learning that aims at producing a large margin classifier. The notion of margin, minimum distance to a decision boundary, has served as the foundation of several theoretically profound and empirically…

Machine Learning · Statistics 2018-12-05 Gamaleldin F. Elsayed , Dilip Krishnan , Hossein Mobahi , Kevin Regan , Samy Bengio

We give a general recipe for derandomising PAC-Bayesian bounds using margins, with the critical ingredient being that our randomised predictions concentrate around some value. The tools we develop straightforwardly lead to margin bounds for…

Machine Learning · Computer Science 2022-02-24 Felix Biggs , Benjamin Guedj

In this work, we study the learning theory of reward modeling with pairwise comparison data using deep neural networks. We establish a novel non-asymptotic regret bound for deep reward estimators in a non-parametric setting, which depends…

Machine Learning · Statistics 2025-05-13 Yuanhang Luo , Yeheng Ge , Ruijian Han , Guohao Shen