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We present a new family of information-theoretic generalization bounds, in which the training loss and the population loss are compared through a jointly convex function. This function is upper-bounded in terms of the disintegrated,…

Machine Learning · Computer Science 2023-03-28 Fredrik Hellström , Giuseppe Durisi

Sandwiched (quantum) $\alpha$-R\'enyi divergence has been recently defined in the independent works of Wilde et al. (arXiv:1306.1586) and M\"uller-Lennert et al (arXiv:1306.3142v1). This new quantum divergence has already found applications…

Quantum Physics · Physics 2013-12-16 Salman Beigi

The generalization bound is a crucial theoretical tool for assessing the generalizability of learning methods and there exist vast literatures on generalizability of normal learning, adversarial learning, and data poisoning. Unlike other…

Machine Learning · Computer Science 2024-06-05 Lijia Yu , Shuang Liu , Yibo Miao , Xiao-Shan Gao , Lijun Zhang

We derive upper bounds on the generalization error of learning algorithms based on their \emph{algorithmic transport cost}: the expected Wasserstein distance between the output hypothesis and the output hypothesis conditioned on an input…

Machine Learning · Statistics 2018-11-09 Jingwei Zhang , Tongliang Liu , Dacheng Tao

Quantum information processing is limited, in practice, to efficiently implementable operations. This motivates the study of quantum divergences that preserve their operational meaning while faithfully capturing these computational…

Quantum Physics · Physics 2025-09-26 Álvaro Yángüez , Thomas A. Hahn , Jan Kochanowski

Bounding the generalization error of a supervised learning algorithm is one of the most important problems in learning theory, and various approaches have been developed. However, existing bounds are often loose and lack of guarantees. As a…

Machine Learning · Computer Science 2021-07-30 Gholamali Aminian , Yuheng Bu , Laura Toni , Miguel R. D. Rodrigues , Gregory Wornell

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

In this paper, we present generalization bounds for the unsupervised risk in the Deep Contrastive Representation Learning framework, which employs deep neural networks as representation functions. We approach this problem from two angles.…

Machine Learning · Statistics 2024-12-20 Nong Minh Hieu , Antoine Ledent , Yunwen Lei , Cheng Yeaw Ku

Change of measure inequalities translate divergences between probability measures into explicit bounds on event probabilities, and play an important role in deriving probabilistic guarantees in learning theory, information theory, and…

Information Theory · Computer Science 2026-05-28 Yanxiao Liu , Yijun Fan , Deniz Gündüz

The overarching goal of this paper is to derive excess risk bounds for learning from exp-concave loss functions in passive and sequential learning settings. Exp-concave loss functions encompass several fundamental problems in machine…

Machine Learning · Computer Science 2014-02-11 Mehrdad Mahdavi , Rong Jin

Exponential generalization bounds with near-tight rates have recently been established for uniformly stable learning algorithms. The notion of uniform stability, however, is stringent in the sense that it is invariant to the data-generating…

Machine Learning · Statistics 2022-06-09 Xiao-Tong Yuan , Ping Li

A fundamental question in theoretical machine learning is generalization. Over the past decades, the PAC-Bayesian approach has been established as a flexible framework to address the generalization capabilities of machine learning…

Machine Learning · Computer Science 2024-03-28 Fredrik Hellström , Giuseppe Durisi , Benjamin Guedj , Maxim Raginsky

Algorithm-dependent generalization error bounds are central to statistical learning theory. A learning algorithm may use a large hypothesis space, but the limited number of iterations controls its model capacity and generalization error.…

Machine Learning · Computer Science 2017-07-20 Wenlong Mou , Liwei Wang , Xiyu Zhai , Kai Zheng

In this paper, we present the Bennett-type generalization bounds of the learning process for i.i.d. samples, and then show that the generalization bounds have a faster rate of convergence than the traditional results. In particular, we…

Machine Learning · Statistics 2013-09-27 Chao Zhang

This PhD thesis combines two of the most exciting research areas of the last decades: quantum computing and machine learning. We introduce dissipative quantum neural networks (DQNNs), which are designed for fully quantum learning tasks, are…

Quantum Physics · Physics 2022-05-18 Kerstin Beer

We present a new family of information-theoretic generalization bounds within the framework of conditional mutual information (CMI). Most of our results are established based on the leave-$m$-out (L$m$O) cross-validation error, with $m$…

Information Theory · Computer Science 2026-05-21 Yang Lu , Matthias Frey , Margreta Kuijper , Jingge Zhu

We consider the problem of transfer learning in an online setting. Different tasks are presented sequentially and processed by a within-task algorithm. We propose a lifelong learning strategy which refines the underlying data representation…

Machine Learning · Statistics 2019-10-14 Pierre Alquier , The Tien Mai , Massimiliano Pontil

In this work, we show that the sample complexity required in quantum learning theory within a general parametric framework, is fundamentally governed by the inverse Fisher information matrix. More specifically, we derive upper and lower…

Quantum Physics · Physics 2026-03-11 Hyukgun Kwon , Seok Hyung Lie , Liang Jiang

Traditional supervised learning aims to train a classifier in the closed-set world, where training and test samples share the same label space. In this paper, we target a more challenging and realistic setting: open-set learning (OSL),…

Machine Learning · Computer Science 2021-07-01 Zhen Fang , Jie Lu , Anjin Liu , Feng Liu , Guangquan Zhang

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