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Recurrent Neural Networks (RNNs) have achieved great success in the prediction of sequential data. However, their theoretical studies are still lagging behind because of their complex interconnected structures. In this paper, we establish a…

Machine Learning · Statistics 2024-11-06 Xuewei Cheng , Ke Huang , Shujie Ma

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 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

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

We develop a new classification framework based on the theory of coherent risk measures and systemic risk. The proposed approach is suitable for multi-class problems when the data is noisy, scarce (relative to the dimension of the problem),…

Machine Learning · Statistics 2026-05-29 Darinka Dentcheva , Xiangyu Tian

The C-bound, introduced in Lacasse et al., gives a tight upper bound on the risk of a binary majority vote classifier. In this work, we present a first step towards extending this work to more complex outputs, by providing generalizations…

Machine Learning · Statistics 2015-01-14 Francois Laviolette , Emilie Morvant , Liva Ralaivola , Jean-Francis Roy

We analyze the practices of reservoir computing in the framework of statistical learning theory. In particular, we derive finite sample upper bounds for the generalization error committed by specific families of reservoir computing systems…

Machine Learning · Computer Science 2019-10-31 Lukas Gonon , Lyudmila Grigoryeva , Juan-Pablo Ortega

When dealing with imbalanced classification data, reweighting the loss function is a standard procedure allowing to equilibrate between the true positive and true negative rates within the risk measure. Despite significant theoretical work…

Machine Learning · Statistics 2024-04-17 Anass Aghbalou , François Portier , Anne Sabourin

In statistical learning theory, determining the sample complexity of realizable binary classification for VC classes was a long-standing open problem. The results of Simon and Hanneke established sharp upper bounds in this setting. However,…

Machine Learning · Computer Science 2023-04-19 Ishaq Aden-Ali , Yeshwanth Cherapanamjeri , Abhishek Shetty , Nikita Zhivotovskiy

We consider a standard binary classification problem. The performance of any binary classifier based on the training data is characterized by the excess risk. We study Bahadur's type exponential bounds on the minimax accuracy confidence…

Machine Learning · Statistics 2011-11-29 N. I. Pentacaput

Due to myriads of classes, designing accurate and efficient classifiers becomes very challenging for multi-class classification. Recent research has shown that class structure learning can greatly facilitate multi-class learning. In this…

Machine Learning · Computer Science 2012-02-20 Jian-Bo Yang , Ivor W. Tsang

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 analyze the local Rademacher complexity of empirical risk minimization (ERM)-based multi-label learning algorithms, and in doing so propose a new algorithm for multi-label learning. Rather than using the trace norm to regularize the…

Machine Learning · Statistics 2014-10-28 Chang Xu , Tongliang Liu , Dacheng Tao , Chao Xu

We study the sample complexity of multiclass prediction in several learning settings. For the PAC setting our analysis reveals a surprising phenomenon: In sharp contrast to binary classification, we show that there exist multiclass…

Machine Learning · Computer Science 2016-04-19 Amit Daniely , Sivan Sabato , Shai Ben-David , Shai Shalev-Shwartz

Here we propose a general theoretical method for analyzing the risk bound in the presence of adversaries. Specifically, we try to fit the adversarial learning problem into the minimax framework. We first show that the original adversarial…

Machine Learning · Statistics 2019-01-25 Zhuozhuo Tu , Jingwei Zhang , Dacheng Tao

A classical condition for fast learning rates is the margin condition, first introduced by Mammen and Tsybakov. We tackle in this paper the problem of adaptivity to this condition in the context of model selection, in a general learning…

Statistics Theory · Mathematics 2011-05-02 Sylvain Arlot , Peter L. Bartlett

This paper formalizes a latent variable inference problem we call {\em supervised pattern discovery}, the goal of which is to find sets of observations that belong to a single ``pattern.'' We discuss two versions of the problem and prove…

Machine Learning · Statistics 2014-02-10 Jonathan H. Huggins , Cynthia Rudin

Advanced classification algorithms are being increasingly used in safety-critical applications like health-care, engineering, etc. In such applications, miss-classifications made by ML algorithms can result in substantial financial or…

Machine Learning · Computer Science 2024-12-06 Disha Ghandwani , Neeraj Sarna , Yuanyuan Li , Yang Lin

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

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