Learning by extended statistical queries and its relation to PAC learning

  • Eli Shamir
  • Clara Shwartzman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 904)


PAC learning from examples is factored so that (i) the membership queries are used to evaluate empirically “statistical queries” — certain expectations of functionals involving the unknown target. (ii) approximate value of these statistical queries are used to compute an output — an approximation of the target.

Kearns' original formulation of statistical queries [we use the abbreviation SQ], is extended here to include as SQ functionals of arbitrary range and order higher than one — second order being the most useful addition. This enables us to capture more ground for casting efficient PAC learning algorithms in SQ form: The important Kushilevitz-Mansour Fourier - based algorithm has an SQ rendition, as well as its derivatives, e.g. Jackson's recent DNF learning.

Efficient evaluation of extended SQ by membership queries, if possible at all, becomes quite intricate. We show, however, that it is usually robust under classification noise.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Eli Shamir
    • 1
  • Clara Shwartzman
    • 1
  1. 1.Institute of Mathematics and Computer ScienceHebrew UniversityJerusalem

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