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The balanced loss is a widely adopted objective for multi-class classification under class imbalance. By assigning equal importance to all classes, regardless of their frequency, it promotes fairness and ensures that minority classes are…

Machine Learning · Computer Science 2026-01-01 Corinna Cortes , Mehryar Mohri , Yutao Zhong

In this paper we refine the process of computing calibration functions for a number of multiclass classification surrogate losses. Calibration functions are a powerful tool for easily converting bounds for the surrogate risk (which can be…

Machine Learning · Statistics 2016-09-22 Bernardo Ávila Pires , Csaba Szepesvári

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 consider composite loss functions for multiclass prediction comprising a proper (i.e., Fisher-consistent) loss over probability distributions and an inverse link function. We establish conditions for their (strong) convexity and explore…

Machine Learning · Computer Science 2012-06-22 Mark Reid , Robert Williamson , Peng Sun

We study consistency properties of surrogate loss functions for general multiclass learning problems, defined by a general multiclass loss matrix. We extend the notion of classification calibration, which has been studied for binary and…

Machine Learning · Computer Science 2015-08-25 Harish G. Ramaswamy , Shivani Agarwal

We propose a novel hybrid loss for multiclass and structured prediction problems that is a convex combination of a log loss for Conditional Random Fields (CRFs) and a multiclass hinge loss for Support Vector Machines (SVMs). We provide a…

Machine Learning · Computer Science 2014-02-11 Qinfeng Shi , Mark Reid , Tiberio Caetano , Anton van den Hengel , Zhenhua Wang

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

PAC-Bayesian bounds have proven to be a valuable tool for deriving generalization bounds and for designing new learning algorithms in machine learning. However, it typically focus on providing generalization bounds with respect to a chosen…

Machine Learning · Statistics 2024-08-19 The Tien Mai

We propose a novel hybrid loss for multiclass and structured prediction problems that is a convex combination of log loss for Conditional Random Fields (CRFs) and a multiclass hinge loss for Support Vector Machines (SVMs). We provide a…

Machine Learning · Computer Science 2010-09-20 Qinfeng Shi , Mark D. Reid , Tiberio Caetano

The notion of margin loss has been central to the development and analysis of algorithms for binary classification. To date, however, there remains no consensus as to the analogue of the margin loss for multiclass classification. In this…

Machine Learning · Statistics 2024-05-20 Yutong Wang , Clayton Scott

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

Via an overparameterized linear model with Gaussian features, we provide conditions for good generalization for multiclass classification of minimum-norm interpolating solutions in an asymptotic setting where both the number of underlying…

Machine Learning · Computer Science 2022-06-06 Vignesh Subramanian , Rahul Arya , Anant Sahai

Medical diagnosis might fail due to bias. In this work, we identified class-feature bias, which refers to models' potential reliance on features that are strongly correlated with only a subset of classes, leading to biased performance and…

Machine Learning · Computer Science 2025-09-03 Lishi Zuo , Man-Wai Mak , Lu Yi , Youzhi Tu

We investigate the problem of multiclass classification with rejection, where a classifier can choose not to make a prediction to avoid critical misclassification. First, we consider an approach based on simultaneous training of a…

Machine Learning · Statistics 2019-10-31 Chenri Ni , Nontawat Charoenphakdee , Junya Honda , Masashi Sugiyama

Classification problems are essential statistical tasks that form the foundation of decision-making across various fields, including patient prognosis and treatment strategies for critical conditions. Consequently, evaluating the…

Methodology · Statistics 2025-03-11 Jun Tamura , Yuki Itaya , Kenichi Hayashi , Kouji Yamamoto

We present a detailed study of surrogate losses and algorithms for multi-label learning, supported by $H$-consistency bounds. We first show that, for the simplest form of multi-label loss (the popular Hamming loss), the well-known…

Machine Learning · Computer Science 2024-07-19 Anqi Mao , Mehryar Mohri , Yutao Zhong

Many classification applications require accurate probability estimates in addition to good class separation but often classifiers are designed focusing only on the latter. Calibration is the process of improving probability estimates by…

Machine Learning · Computer Science 2020-01-31 Tuomo Alasalmi , Jaakko Suutala , Heli Koskimäki , Juha Röning

We address the problem of aggregating an ensemble of predictors with known loss bounds in a semi-supervised binary classification setting, to minimize prediction loss incurred on the unlabeled data. We find the minimax optimal predictions…

Machine Learning · Computer Science 2016-11-08 Akshay Balsubramani , Yoav Freund

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

The Softmax loss is one of the most widely employed surrogate objectives for classification and ranking tasks. To elucidate its theoretical properties, the Fenchel-Young framework situates it as a canonical instance within a broad family of…

Machine Learning · Computer Science 2026-02-02 Yuanhao Pu , Defu Lian , Enhong Chen
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