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.ICDT.2019.24
URN: urn:nbn:de:0030-drops-103261
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10326/
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Grienenberger, Emilie ; Ritzert, Martin

Learning Definable Hypotheses on Trees

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LIPIcs-ICDT-2019-24.pdf (0.5 MB)

Abstract

We study the problem of learning properties of nodes in tree structures. Those properties are specified by logical formulas, such as formulas from first-order or monadic second-order logic. We think of the tree as a database encoding a large dataset and therefore aim for learning algorithms which depend at most sublinearly on the size of the tree. We present a learning algorithm for quantifier-free formulas where the running time only depends polynomially on the number of training examples, but not on the size of the background structure. By a previous result on strings we know that for general first-order or monadic second-order (MSO) formulas a sublinear running time cannot be achieved. However, we show that by building an index on the tree in a linear time preprocessing phase, we can achieve a learning algorithm for MSO formulas with a logarithmic learning phase.

BibTeX - Entry

@InProceedings{grienenberger_et_al:LIPIcs:2019:10326,
  author =	{Emilie Grienenberger and Martin Ritzert},
  title =	{{Learning Definable Hypotheses on Trees}},
  booktitle =	{22nd International Conference on Database Theory (ICDT 2019)},
  pages =	{24:1--24:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-101-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{127},
  editor =	{Pablo Barcelo and Marco Calautti},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10326},
  doi =		{10.4230/LIPIcs.ICDT.2019.24},
  annote =	{Keywords: monadic second-order logic, trees, query learning}
}

Keywords: monadic second-order logic, trees, query learning
Collection: 22nd International Conference on Database Theory (ICDT 2019)
Issue Date: 2019
Date of publication: 19.03.2019

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