License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2016.63
URN: urn:nbn:de:0030-drops-64750
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6475/
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Labai, Nadia ; Makowsky, Johann A.

On the Exact Learnability of Graph Parameters: The Case of Partition Functions

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LIPIcs-MFCS-2016-63.pdf (0.6 MB)

Abstract

We study the exact learnability of real valued graph parameters f which are known to be representable as partition functions which count the number of weighted homomorphisms into a graph H with vertex weights alpha and edge weights beta. M. Freedman, L. Lovasz and A. Schrijver have given a characterization of these graph parameters in terms of the k-connection matrices C(f,k) of f. Our model of learnability is based on D. Angluin's model of exact learning using membership and equivalence queries. Given such a graph parameter f, the learner can ask for the values of f for graphs of their choice, and they can formulate hypotheses in terms of the connection matrices C(f,k) of f. The teacher can accept the hypothesis as correct, or provide a counterexample consisting of a graph. Our main result shows that in this scenario, a very large class of partition functions,
the rigid partition functions, can be learned in time polynomial in the size of H and the size of the largest counterexample in the Blum-Shub-Smale model of computation over the reals with unit cost.

BibTeX - Entry

@InProceedings{labai_et_al:LIPIcs:2016:6475,
  author =	{Nadia Labai and Johann A. Makowsky},
  title =	{{On the Exact Learnability of Graph Parameters: The Case of Partition Functions}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{63:1--63:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Piotr Faliszewski and Anca Muscholl and Rolf Niedermeier},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6475},
  URN =		{urn:nbn:de:0030-drops-64750},
  doi =		{10.4230/LIPIcs.MFCS.2016.63},
  annote =	{Keywords: exact learning, partition function, weighted homomorphism, connection matrices}
}

Keywords: exact learning, partition function, weighted homomorphism, connection matrices
Collection: 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)
Issue Date: 2016
Date of publication: 19.08.2016

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