On ψ Learning

Xiaotong Shen, George C. Tseng, Xuegong Zhang, Wing Hung Wong

Research output: Contribution to journalArticlepeer-review

135 Scopus citations


The concept of large margins have been recognized as an important principle in analyzing learning methodologies, including boosting, neural networks, and support vector machines (SVMs). However, this concept alone is not adequate for learning in nonseparable cases. We propose a learning methodology, called ψ-learning, that is derived from a direct consideration of generalization errors. We provide a theory for ψ-learning and show that it essentially attains the optimal rates of convergence in two learning examples. Finally, results from simulation studies and from breast cancer classification confirm the ability of ψ-learning to outperform SVM in generalization.

Original languageEnglish (US)
Pages (from-to)724-734
Number of pages11
JournalJournal of the American Statistical Association
Issue number463
StatePublished - Sep 2003

Bibliographical note

Copyright 2008 Elsevier B.V., All rights reserved.


  • Classification
  • Generalization error
  • Machine learning
  • Margins
  • Metric entropy
  • Support vector machine


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