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We study the key framework of learning with abstention in the multi-class classification setting. In this setting, the learner can choose to abstain from making a prediction with some pre-defined cost. We present a series of new theoretical…

Machine Learning · Computer Science 2024-04-02 Anqi Mao , Mehryar Mohri , Yutao Zhong

Modern machine learning approaches to classification, including AdaBoost, support vector machines, and deep neural networks, utilize surrogate loss techniques to circumvent the computational complexity of minimizing empirical classification…

Econometrics · Economics 2023-07-26 Toru Kitagawa , Shosei Sakaguchi , Aleksey Tetenov

We study the consistency of surrogate risks for robust binary classification. It is common to learn robust classifiers by adversarial training, which seeks to minimize the expected $0$-$1$ loss when each example can be maliciously corrupted…

Machine Learning · Computer Science 2025-10-09 Natalie Frank , Jonathan Niles-Weed

In multiclass classification over $n$ outcomes, the outcomes must be embedded into the reals with dimension at least $n-1$ in order to design a consistent surrogate loss that leads to the "correct" classification, regardless of the data…

Machine Learning · Computer Science 2026-01-21 Enrique Nueve , Bo Waggoner , Dhamma Kimpara , Jessie Finocchiaro

We carefully study how well minimizing convex surrogate loss functions, corresponds to minimizing the misclassification error rate for the problem of binary classification with linear predictors. In particular, we show that amongst all…

Machine Learning · Computer Science 2012-07-03 Shai Ben-David , David Loker , Nathan Srebro , Karthik Sridharan

We study the problem of classification with a reject option for a fixed predictor, applicable in natural language processing. We introduce a new problem formulation for this scenario, and an algorithm minimizing a new surrogate loss…

Machine Learning · Computer Science 2023-02-01 Christopher Mohri , Daniel Andor , Eunsol Choi , Michael Collins

We propose a robust adversarial prediction framework for general multiclass classification. Our method seeks predictive distributions that robustly optimize non-convex and non-continuous multiclass loss metrics against the worst-case…

Large language models (LLMs) have achieved remarkable performance but face critical challenges: hallucinations and high inference costs. Leveraging multiple experts offers a solution: deferring uncertain inputs to more capable experts…

Machine Learning · Computer Science 2025-12-30 Anqi Mao

Learning with abstention is a key scenario where the learner can abstain from making a prediction at some cost. In this paper, we analyze the score-based formulation of learning with abstention in the multi-class classification setting. We…

Machine Learning · Computer Science 2024-04-02 Anqi Mao , Mehryar Mohri , Yutao Zhong

Learning with rejection is an important framework that can refrain from making predictions to avoid critical mispredictions by balancing between prediction and rejection. Previous studies on cost-based rejection only focused on the…

Machine Learning · Computer Science 2023-11-09 Xin Cheng , Yuzhou Cao , Haobo Wang , Hongxin Wei , Bo An , Lei Feng

Top-$k$ classification is a generalization of multiclass classification used widely in information retrieval, image classification, and other extreme classification settings. Several hinge-like (piecewise-linear) surrogates have been…

Machine Learning · Computer Science 2022-07-20 Jessie Finocchiaro , Rafael Frongillo , Emma Goodwill , Anish Thilagar

Commonly used classification algorithms in machine learning, such as support vector machines, minimize a convex surrogate loss on training examples. In practice, these algorithms are surprisingly robust to errors in the training data. In…

Machine Learning · Computer Science 2020-12-03 Kunal Talwar

In this paper, we study the problem of consistency in the context of adversarial examples. Specifically, we tackle the following question: can surrogate losses still be used as a proxy for minimizing the $0/1$ loss in the presence of an…

Machine Learning · Computer Science 2022-05-23 Laurent Meunier , Raphaël Ettedgui , Rafael Pinot , Yann Chevaleyre , Jamal Atif

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

Robustness towards adversarial attacks is a vital property for classifiers in several applications such as autonomous driving, medical diagnosis, etc. Also, in such scenarios, where the cost of misclassification is very high, knowing when…

Machine Learning · Computer Science 2024-10-15 Vrund Shah , Tejas Chaudhari , Naresh Manwani

The Lov\'asz hinge is a convex surrogate recently proposed for structured binary classification, in which $k$ binary predictions are made simultaneously and the error is judged by a submodular set function. Despite its wide usage in image…

Machine Learning · Computer Science 2022-03-18 Jessie Finocchiaro , Rafael Frongillo , Enrique Nueve

We provide novel theoretical insights on structured prediction in the context of efficient convex surrogate loss minimization with consistency guarantees. For any task loss, we construct a convex surrogate that can be optimized via…

Machine Learning · Computer Science 2018-01-30 Anton Osokin , Francis Bach , Simon Lacoste-Julien

The top-$k$ error is often employed to evaluate performance for challenging classification tasks in computer vision as it is designed to compensate for ambiguity in ground truth labels. This practical success motivates our theoretical…

Machine Learning · Computer Science 2020-07-09 Forest Yang , Sanmi Koyejo

Learning with rejection has been a prototypical model for studying the human-AI interaction on prediction tasks. Upon the arrival of a sample instance, the model first uses a rejector to decide whether to accept and use the AI predictor to…

Machine Learning · Computer Science 2024-04-23 Xiaocheng Li , Shang Liu , Chunlin Sun , Hanzhao Wang

Classification is one of the most important tasks of machine learning. Although the most well studied model is the two-class problem, in many scenarios there is the opportunity to label critical items for manual revision, instead of trying…

Computer Vision and Pattern Recognition · Computer Science 2011-07-18 Ricardo Sousa , Jaime S. Cardoso
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