Apportioned margin approach for cost sensitive large margin classifiers

• Published in: Annals of mathematics and artificial intelligence Vol. 89; no. 12; pp. 1215 - 1235
• Main Authors: Gottlieb, Lee-Ad, Kaufman, Eran, Kontorovich, Aryeh
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.12.2021; Springer; Springer Nature B.V
• Subjects: Artificial Intelligence; Classification; Complex Systems; Computer Science; Economic aspects; Mathematics; Neural networks; Optimization; Regular Submission; Support vector machines; Multi-class classification; Asymmetric cost; Linear classifiers; 68Q32
• ISSN: 1012-2443; 1573-7470
• DOI: 10.1007/s10472-021-09776-w

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 apportioned margin framework to address this problem, which enables an efficient margin shift between classes that share the same boundary. The decision boundary between all pairs of classes divides the margin between them in accordance with a given prioritization vector, which yields a tighter error bound for the important classes while also reducing the overall out-of-sample error. In addition to demonstrating an efficient implementation of our framework, we derive generalization bounds, demonstrate Fisher consistency, adapt the framework to Mercer’s kernel and to neural networks, and report promising empirical results on all accounts.