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DOI: 10.4230/LIPIcs.STACS.2011.320
Measuring Learning Complexity with Criteria Epitomizers

Authors: John Case and Timo Koetzing

Published in: LIPIcs, Volume 9, 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)

Abstract
In prior papers, beginning with the seminal work by Freivalds et al. 1995, the notion of intrinsic complexity is used to analyze the learning complexity of sets of functions in a Gold-style learning setting. Herein are pointed out some weaknesses of this notion. Offered is an alternative based on epitomizing sets of functions -- sets, which are learnable under a given learning criterion, but not under other criteria which are not at least as powerful. To capture the idea of epitomizing sets, new reducibility notions are given based on robust learning (closure of learning under certain classes of operators). Various degrees of epitomizing sets are characterized as the sets complete with respect to corresponding reducibility notions! These characterizations also provide an easy method for showing sets to be epitomizers, and they are, then, employed to prove several sets to be epitomizing. Furthermore, a scheme is provided to generate easily very strong epitomizers for a multitude of learning criteria. These strong epitomizers are so-called self-learning sets, previously applied by Case & Koetzing, 2010. These strong epitomizers can be generated and employed in a myriad of settings to witness the strict separation in learning power between the criteria so epitomized and other not as powerful criteria!
Cite as

John Case and Timo Koetzing. Measuring Learning Complexity with Criteria Epitomizers. In 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 9, pp. 320-331, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{case_et_al:LIPIcs.STACS.2011.320,
  author =	{Case, John and Koetzing, Timo},
  title =	{{Measuring Learning Complexity with Criteria Epitomizers}},
  booktitle =	{28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)},
  pages =	{320--331},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-25-5},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{9},
  editor =	{Schwentick, Thomas and D\"{u}rr, Christoph},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2011.320},
  URN =		{urn:nbn:de:0030-drops-30232},
  doi =		{10.4230/LIPIcs.STACS.2011.320},
  annote =	{Keywords: Algorithmic Learning Theory, Learning Complexity, Robustness in Learning}
}
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