Multicategory ψ-learning

Yufeng Liu, Xiaotong Shen

Research output: Contribution to journalArticle

108 Scopus citations


In binary classification, margin-based techniques usually deliver high performance. As a result, a multicategory problem is often treated as a sequence of binary classifications. In the absence of a dominating class, this treatment may be suboptimal and may yield poor performance, such as for support vector machines (SVMs). We propose a novel multicategory generalization of ψ-learning that treats all classes simultaneously. The new generalization eliminates this potential problem while at the same time retaining the desirable properties of its binary counterpart. We develop a statistical learning theory for the proposed methodology and obtain fast convergence rates for both linear and nonlinear learning examples. We demonstrate the operational characteristics of this method through a simulation. Our results indicate that the proposed methodology can deliver accurate class prediction and is more robust against extreme observations than its SVM counterpart.

Original languageEnglish (US)
Pages (from-to)500-509
Number of pages10
JournalJournal of the American Statistical Association
Issue number474
StatePublished - Jun 2006


  • Generalization error
  • Nonconvex minimization
  • Supervised learning
  • Support vectors

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