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Related papers: Maximum Margin Multiclass Nearest Neighbors

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Recent advances in large-margin classification of data residing in general metric spaces (rather than Hilbert spaces) enable classification under various natural metrics, such as string edit and earthmover distance. A general framework…

Machine Learning · Computer Science 2014-07-14 Lee-Ad Gottlieb , Aryeh Kontorovich , Robert Krauthgamer

For linear classifiers, the relationship between (normalized) output margin and generalization is captured in a clear and simple bound -- a large output margin implies good generalization. Unfortunately, for deep models, this relationship…

Machine Learning · Computer Science 2021-06-17 Colin Wei , Tengyu Ma

In this paper, we propose the Lipschitz margin ratio and a new metric learning framework for classification through maximizing the ratio. This framework enables the integration of both the inter-class margin and the intra-class dispersion,…

Machine Learning · Computer Science 2018-02-13 Mingzhi Dong , Xiaochen Yang , Yang Wu , Jing-Hao Xue

We consider a model of robust learning in an adversarial environment. The learner gets uncorrupted training data with access to possible corruptions that may be affected by the adversary during testing. The learner's goal is to build a…

Machine Learning · Computer Science 2022-07-04 Idan Attias , Aryeh Kontorovich , Yishay Mansour

We consider the problem of cost sensitive multiclass classification, where we would like to increase the sensitivity of an important class at the expense of a less important one. We adopt an {\em apportioned margin} framework to address…

Machine Learning · Computer Science 2020-02-05 Lee-Ad Gottlieb , Eran Kaufman , Aryeh Kontorovich

We study the generalisation properties of majority voting on finite ensembles of classifiers, proving margin-based generalisation bounds via the PAC-Bayes theory. These provide state-of-the-art guarantees on a number of classification…

Machine Learning · Computer Science 2022-10-21 Felix Biggs , Valentina Zantedeschi , Benjamin Guedj

Logistic models are commonly used for binary classification tasks. The success of such models has often been attributed to their connection to maximum-likelihood estimators. It has been shown that gradient descent algorithm, when applied on…

Machine Learning · Statistics 2020-10-30 Fariborz Salehi , Ehsan Abbasi , Babak Hassibi

Maximum margin binary classification is one of the most fundamental algorithms in machine learning, yet the role of featurization maps and the high-dimensional asymptotics of the misclassification error for non-Gaussian features are still…

Statistics Theory · Mathematics 2023-10-03 Andrea Montanari , Feng Ruan , Basil Saeed , Youngtak Sohn

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

This paper proposes a new probabilistic classification algorithm using a Markov random field approach. The joint distribution of class labels is explicitly modelled using the distances between feature vectors. Intuitively, a class label…

Computation · Statistics 2010-06-02 Nial Friel , Anthony N. Pettitt

We study the problem of learning local metrics for nearest neighbor classification. Most previous works on local metric learning learn a number of local unrelated metrics. While this "independence" approach delivers an increased flexibility…

Machine Learning · Computer Science 2012-09-17 Jun Wang , Adam Woznica , Alexandros Kalousis

Modern machine learning systems such as deep neural networks are often highly over-parameterized so that they can fit the noisy training data exactly, yet they can still achieve small test errors in practice. In this paper, we study this…

Machine Learning · Computer Science 2022-01-04 Yuan Cao , Quanquan Gu , Mikhail Belkin

We study the typical learning properties of the recently introduced Soft Margin Classifiers (SMCs), learning realizable and unrealizable tasks, with the tools of Statistical Mechanics. We derive analytically the behaviour of the learning…

Disordered Systems and Neural Networks · Physics 2009-11-07 Sebastian Risau-Gusman , Mirta B. Gordon

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

Learning a robust classifier from a few samples remains a key challenge in machine learning. A major thrust of research has been focused on developing $k$-nearest neighbor ($k$-NN) based algorithms combined with metric learning that…

Machine Learning · Statistics 2022-02-17 Shixiang Zhu , Liyan Xie , Minghe Zhang , Rui Gao , Yao Xie

In this paper, we study the data-dependent convergence and generalization behavior of gradient methods for neural networks with smooth activation. Our first result is a novel bound on the excess risk of deep networks trained by the logistic…

Machine Learning · Computer Science 2024-12-09 Hossein Taheri , Christos Thrampoulidis , Arya Mazumdar

We consider the problem of multi-class classification and a stochastic opti- mization approach to it. We derive risk bounds for stochastic mirror descent algorithm and provide examples of set geometries that make the use of the algorithm…

Optimization and Control · Mathematics 2016-12-09 Daria Reshetova

We prove bounds on the population risk of the maximum margin algorithm for two-class linear classification. For linearly separable training data, the maximum margin algorithm has been shown in previous work to be equivalent to a limit of…

Machine Learning · Statistics 2021-06-03 Niladri S. Chatterji , Philip M. Long

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

Motivated by a wide variety of applications, ranging from stochastic optimization to dimension reduction through variable selection, the problem of estimating gradients accurately is of crucial importance in statistics and learning theory.…

Machine Learning · Computer Science 2020-06-29 Guillaume Ausset , Stephan Clémençon , François Portier