Exploring learnability between exact and PAC

Authors:
Nader H. Bshouty;Jeffrey C. Jackson;Christino Tamon
Affiliations:
Department of Computer Science, Technion, Haifa 32000, Israel;Mathematics and Computer Science Department, Duquesne University, Pittsburgh PA, USA;Department of Mathematics and Computer Science, Clarkson University, 373 Science Center, Box 5815, Potsdam, NY 13699-5815, USA
Venue:
Journal of Computer and System Sciences - Special issue on COLT 2002
Year:
2005

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Abstract

We study a model of probably exactly correct (PExact) learning that can be viewed either as the Exact model (learning from equivalence queries only) relaxed so that counterexamples to equivalence queries are distributionally drawn rather than adversarially chosen or as the probably approximately correct (PAC) model strengthened to require a perfect hypothesis. We also introduce a model of probably almost exactly correct (PAExact) learning that requires a hypothesis with negligible error and thus lies between the PExact and PAC models. Unlike the Exact and PExact models, PAExact learning is applicable to classes of functions defined over infinite instance spaces. We obtain a number of separation results between these models. Of particular note are some positive results for efficient parallel learning in the PAExact model, which stand in stark contrast to earlier negative results for efficient parallel Exact learning.