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The minimum error minimax probability machine

Publication ,  Journal Article
Huang, K; Yang, H; King, I; Lyu, MR; Chan, L
Published in: Journal of Machine Learning Research
October 1, 2004

We construct a distribution-free Bayes optimal classifier called the Minimum Error Minimax Probability Machine (MEMPM) in a worst-case setting, i.e., under all possible choices of class-conditional densities with a given mean and covariance matrix. By assuming no specific distributions for the data, our model is thus distinguished from traditional Bayes optimal approaches, where an assumption on the data distribution is a must. This model is extended from the Minimax Probability Machine (MPM), a recently-proposed novel classifier, and is demonstrated to be the general case of MPM. Moreover, it includes another special case named the Biased Minimax Probability Machine, which is appropriate for handling biased classification. One appealing feature of MEMPM is that it contains an explicit performance indicator, i.e., a lower bound on the worst-case accuracy, which is shown to be tighter than that of MPM. We provide conditions under which the worst-case Bayes optimal classifier converges to the Bayes optimal classifier. We demonstrate how to apply a more general statistical framework to estimate model input parameters robustly. We also show how to extend our model to nonlinear classification by exploiting kernelization techniques. A series of experiments on both synthetic data sets and real world benchmark data sets validates our proposition and demonstrates the effectiveness of our model.

Duke Scholars

Published In

Journal of Machine Learning Research

EISSN

1533-7928

ISSN

1532-4435

Publication Date

October 1, 2004

Volume

5

Start / End Page

1253 / 1286

Related Subject Headings

  • Artificial Intelligence & Image Processing
  • 4905 Statistics
  • 4611 Machine learning
  • 17 Psychology and Cognitive Sciences
  • 08 Information and Computing Sciences
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Huang, K., Yang, H., King, I., Lyu, M. R., & Chan, L. (2004). The minimum error minimax probability machine. Journal of Machine Learning Research, 5, 1253–1286.
Huang, K., H. Yang, I. King, M. R. Lyu, and L. Chan. “The minimum error minimax probability machine.” Journal of Machine Learning Research 5 (October 1, 2004): 1253–86.
Huang K, Yang H, King I, Lyu MR, Chan L. The minimum error minimax probability machine. Journal of Machine Learning Research. 2004 Oct 1;5:1253–86.
Huang, K., et al. “The minimum error minimax probability machine.” Journal of Machine Learning Research, vol. 5, Oct. 2004, pp. 1253–86.
Huang K, Yang H, King I, Lyu MR, Chan L. The minimum error minimax probability machine. Journal of Machine Learning Research. 2004 Oct 1;5:1253–1286.

Published In

Journal of Machine Learning Research

EISSN

1533-7928

ISSN

1532-4435

Publication Date

October 1, 2004

Volume

5

Start / End Page

1253 / 1286

Related Subject Headings

  • Artificial Intelligence & Image Processing
  • 4905 Statistics
  • 4611 Machine learning
  • 17 Psychology and Cognitive Sciences
  • 08 Information and Computing Sciences