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We study losses for binary classification and class probability estimation and extend the understanding of them from margin losses to general composite losses which are the composition of a proper loss with a link function. We characterise…

Machine Learning · Statistics 2009-12-18 Mark D. Reid , Robert C. Williamson

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

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

This paper studies binary classification problem associated with a family of loss functions called large-margin unified machines (LUM), which offers a natural bridge between distribution-based likelihood approaches and margin-based…

Machine Learning · Statistics 2019-08-14 Jun Fan , Dao-Hong Xiang

This paper explores connections between margin-based loss functions and consistency in binary classification and regression applications. It is shown that a large class of margin-based loss functions for binary classification/regression…

Machine Learning · Statistics 2023-01-30 Jeffrey Buzas

We develop new approaches in multi-class settings for constructing proper scoring rules and hinge-like losses and establishing corresponding regret bounds with respect to the zero-one or cost-weighted classification loss. Our construction…

Statistics Theory · Mathematics 2021-05-18 Zhiqiang Tan , Xinwei Zhang

In many real applications of statistical learning, a decision made from misclassification can be too costly to afford; in this case, a reject option, which defers the decision until further investigation is conducted, is often preferred. In…

Machine Learning · Statistics 2017-01-10 Chong Zhang , Wenbo Wang , Xingye Qiao

We provide a unifying view of statistical information measures, multi-way Bayesian hypothesis testing, loss functions for multi-class classification problems, and multi-distribution $f$-divergences, elaborating equivalence results between…

Statistics Theory · Mathematics 2017-09-12 John C. Duchi , Khashayar Khosravi , Feng Ruan

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

Loss functions drive the optimization of machine learning algorithms. The choice of a loss function can have a significant impact on the training of a model, and how the model learns the data. Binary classification is one of the major…

Machine Learning · Computer Science 2022-11-02 Rayan Wali

One of the main challenges for feature representation in deep learning-based classification is the design of appropriate loss functions that exhibit strong discriminative power. The classical softmax loss does not explicitly encourage…

Computer Vision and Pattern Recognition · Computer Science 2022-06-24 Xiong Zhou , Xianming Liu , Deming Zhai , Junjun Jiang , Xin Gao , Xiangyang Ji

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

Real-world object classes appear in imbalanced ratios. This poses a significant challenge for classifiers which get biased towards frequent classes. We hypothesize that improving the generalization capability of a classifier should improve…

Computer Vision and Pattern Recognition · Computer Science 2019-01-24 Munawar Hayat , Salman Khan , Waqas Zamir , Jianbing Shen , Ling Shao

In the supervised binary classification setting, score-oriented losses have been introduced with the aim of optimizing a chosen performance metric directly during the training phase, thus avoiding \textit{a posteriori} threshold tuning. To…

Machine Learning · Computer Science 2025-12-01 Francesco Marchetti , Edoardo Legnaro , Sabrina Guastavino

Despite the enormous success of machine learning models in various applications, most of these models lack resilience to (even small) perturbations in their input data. Hence, new methods to robustify machine learning models seem very…

Machine Learning · Computer Science 2020-10-30 Fariborz Salehi , Babak Hassibi

This paper introduces a negative margin loss to metric learning based few-shot learning methods. The negative margin loss significantly outperforms regular softmax loss, and achieves state-of-the-art accuracy on three standard few-shot…

Computer Vision and Pattern Recognition · Computer Science 2020-03-27 Bin Liu , Yue Cao , Yutong Lin , Qi Li , Zheng Zhang , Mingsheng Long , Han Hu

We consider the problem of online multiclass classification with partial feedback, where an algorithm predicts a class for a new instance in each round and only receives its correctness. Although several methods have been developed for this…

Machine Learning · Computer Science 2019-02-05 Takuo Kaneko , Issei Sato , Masashi Sugiyama

Metric learning seeks perceptual embeddings where visually similar instances are close and dissimilar instances are apart, but learned representations can be sub-optimal when the distribution of intra-class samples is diverse and distinct…

Machine Learning · Computer Science 2021-08-30 Elad Levi , Tete Xiao , Xiaolong Wang , Trevor Darrell

Fisher-consistent loss functions play a fundamental role in the construction of successful binary margin-based classifiers. In this paper we establish the Fisher-consistency condition for multicategory classification problems. Our approach…

Applications · Statistics 2009-01-27 Hui Zou , Ji Zhu , Trevor Hastie

Class imbalance remains a major challenge in machine learning, especially in multi-class problems with long-tailed distributions. Existing methods, such as data resampling, cost-sensitive techniques, and logistic loss modifications, though…

Machine Learning · Computer Science 2025-12-30 Corinna Cortes , Anqi Mao , Mehryar Mohri , Yutao Zhong
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