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Improved Generalization via Tolerant Training

Author

Listed:
  • W. N. Street

    (Oklahoma State University)

  • O. L. Mangasarian

    (University of Wisconsin)

Abstract

Theoretical and computational justification is given for improved generalization when the training set is learned with less accuracy. The model used for this investigation is a simple linear one. It is shown that learning a training set with a tolerance τ improves generalization, over zero-tolerance training, for any testing set satisfying a certain closeness condition to the training set. These results, obtained via a mathematical programming formulation, are placed in the context of some well-known machine learning results. Computational confirmation of improved generalization is given for linear systems (including nine of the twelve real-world data sets tested), as well as for nonlinear systems such as neural networks for which no theoretical results are available at present. In particular, the tolerant training method improves generalization on noisy, sparse, and overparameterized problems.

Suggested Citation

  • W. N. Street & O. L. Mangasarian, 1998. "Improved Generalization via Tolerant Training," Journal of Optimization Theory and Applications, Springer, vol. 96(2), pages 259-279, February.
    • Handle: RePEc:spr:joptap:v:96:y:1998:i:2:d:10.1023_a:1022664513146
    DOI: 10.1023/A:1022664513146
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    References listed on IDEAS

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    1. Harrison, David Jr. & Rubinfeld, Daniel L., 1978. "Hedonic housing prices and the demand for clean air," Journal of Environmental Economics and Management, Elsevier, vol. 5(1), pages 81-102, March.
    2. Olvi L. Mangasarian & W. Nick Street & William H. Wolberg, 1995. "Breast Cancer Diagnosis and Prognosis Via Linear Programming," Operations Research, INFORMS, vol. 43(4), pages 570-577, August.
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    Cited by:

    1. P. S. Bradley & Usama M. Fayyad & O. L. Mangasarian, 1999. "Mathematical Programming for Data Mining: Formulations and Challenges," INFORMS Journal on Computing, INFORMS, vol. 11(3), pages 217-238, August.
    2. A. Astorino & M. Gaudioso, 2002. "Polyhedral Separability Through Successive LP," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 265-293, February.

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