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Learning Definable Hypotheses on Trees

Authors Emilie Grienenberger, Martin Ritzert

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Author Details

Emilie Grienenberger
  • ENS Paris-Saclay, 61 Avenue du Président Wilson, 94230 Cachan, France
Martin Ritzert
  • RWTH Aachen University, Templergraben 55, 52062 Aachen, Germany

Funding

  • Ritzert, Martin: This work is supported by the German research council (DFG) Research Training Group 2236 UnRAVeL.

Cite As Get BibTex

Emilie Grienenberger and Martin Ritzert. Learning Definable Hypotheses on Trees. In 22nd International Conference on Database Theory (ICDT 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 127, pp. 24:1-24:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.ICDT.2019.24

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic
Keywords
  • monadic second-order logic
  • trees
  • query learning

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