Unified Binary and Multiclass Margin-Based Classification
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 work, we show that a broad range of multiclass loss functions, including many popular ones, can be expressed in the relative margin form, a generalization of the margin form of binary losses. The relative margin form is broadly useful for understanding and analyzing multiclass losses as shown by our prior work (Wang and Scott, 2020, 2021). To further demonstrate the utility of this way of expressing multiclass losses, we use it to extend the seminal result of Bartlett et al. (2006) on classification-calibration of binary margin losses to multiclass. We then analyze the class of Fenchel-Young losses, and expand the set of these losses that are known to be classification-calibrated.
Code (0)
등록된 구현이 없습니다.
Tasks
Binary ClassificationClassificationFormMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Multiclass learning with margin: exponential rates with no bias-variance trade-off
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 exponenti…
ClassificationMulticlass Graph-Based Large Margin Classifiers: Unified Approach for Support Vectors and Neural Networks
While large margin classifiers are originally an outcome of an optimization framework, support vectors (SVs) can be obtained from geometric approaches. This article presents advances in the use of Gabriel graphs (GGs) in…
A Unified Framework for Multiclass and Multilabel Support Vector Machines
We propose a novel integrated formulation for multiclass and multilabel support vector machines (SVMs). A number of approaches have been proposed to extend the original binary SVM to an all-in-one multiclass SVM. However…
Convex Optimization for Binary Classifier Aggregation in Multiclass Problems
Multiclass problems are often decomposed into multiple binary problems that are solved by individual binary classifiers whose results are integrated into a final answer. Various methods, including all-pairs (APs), one-ve…
The Multimarginal Optimal Transport Formulation of Adversarial Multiclass Classification
We study a family of adversarial multiclass classification problems and provide equivalent reformulations in terms of: 1) a family of generalized barycenter problems introduced in the paper and 2) a family of multimargin…
Binary ClassificationClassificationRobust classification