eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-03-19
24:1
24:18
10.4230/LIPIcs.ICDT.2019.24
article
Learning Definable Hypotheses on Trees
Grienenberger, Emilie
1
Ritzert, Martin
2
ENS Paris-Saclay, 61 Avenue du Président Wilson, 94230 Cachan, France
RWTH Aachen University, Templergraben 55, 52062 Aachen, Germany
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol127-icdt2019/LIPIcs.ICDT.2019.24/LIPIcs.ICDT.2019.24.pdf
monadic second-order logic
trees
query learning