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Neural Discriminant Analysis

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Algorithmic Learning Theory (ALT 1993)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 744))

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Abstract

Statistical Discriminant Analysis is a classical technique in pattern matching with applications for classification problems and more general decision tasks. In this paper, we use a specific class of discriminant functions which we call product discriminant functions, or simply PDF's. Our main results for PDF's are the following:

  • They are quite expressive, e.g., probability distributions defined by Chow-Expansions, Unique Probabilistic Automata or Unique Markov Models can also succinctly be written as PDF's.

  • It is possible to obtain with high confidence almost optimal decisions for classification problems which can be modelled by PDF's. The number of training examples needed for that is bounded by a polynomial of low degree (in the relevant parameters).

  • The evaluation of the training examples can be implemented on shallow neural nets.

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References

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Author information

Authors and Affiliations

  1. Siemens Corporate Research, Otto-Hahn-Ring 6, W-8000, München 83

    Jorge Ricardo Cuellar

  2. Fachbereich Informatik, Universität Dortmund, W-4600, Dortmund 50

    Hans Ulrich Simon

Authors
  1. Jorge Ricardo Cuellar
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  2. Hans Ulrich Simon
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Editor information

Klaus P. Jantke Shigenobu Kobayashi Etsuji Tomita Takashi Yokomori

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© 1993 Springer-Verlag Berlin Heidelberg

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Cuellar, J.R., Simon, H.U. (1993). Neural Discriminant Analysis. In: Jantke, K.P., Kobayashi, S., Tomita, E., Yokomori, T. (eds) Algorithmic Learning Theory. ALT 1993. Lecture Notes in Computer Science, vol 744. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57370-4_50

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  • DOI: https://doi.org/10.1007/3-540-57370-4_50

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57370-8

  • Online ISBN: 978-3-540-48096-9

  • eBook Packages: Springer Book Archive

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