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Learning from incomplete boundary queries using split graphs and hypergraphs

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Computational Learning Theory (EuroCOLT 1997)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1208))

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Abstract

We consider learnability with membership queries in the presence of incomplete information. In the incomplete boundary query model introduced by Blum et al. [7], it is assumed that membership queries on instances near the boundary of the target concept may receive a “don't know” answer.

We show that zero-one threshold functions are efficiently learnable in this model. The learning algorithm uses split graphs when the boundary region has radius 1, and their generalization to split hypergraphs (for which we give a split-finding algorithm) when the boundary region has constant radius greater than 1. We use a notion of indistinguishability of concepts that is appropriate for this model.

Partially supported by NSF grant CCR-9314258.

Partially supported by NSF grant CCR-9208170, OTKA grant T-14228, and Phare TDQM grant 9305-02/1022 (ILP2/HUN).

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Authors and Affiliations

  1. Dept. of EE & Computer Science, University of Illinois at Chicago, 851 S. Morgan St. Rm 1120, 60607-7053, Chicago, IL, USA

    Robert H. Sloan

  2. Dept. of Mathematics, Stat., & Computer Science, University of Illinois at Chicago, USA

    György Turán

  3. Research Group on Artificial Intelligence, Hungarian Academy of Sciences, Hungary

    György Turán

Authors
  1. Robert H. Sloan
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  2. György Turán
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Shai Ben-David

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© 1997 Springer-Verlag Berlin Heidelberg

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Sloan, R.H., Turán, G. (1997). Learning from incomplete boundary queries using split graphs and hypergraphs. In: Ben-David, S. (eds) Computational Learning Theory. EuroCOLT 1997. Lecture Notes in Computer Science, vol 1208. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62685-9_5

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  • DOI: https://doi.org/10.1007/3-540-62685-9_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62685-5

  • Online ISBN: 978-3-540-68431-2

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