A Property Testing Framework for the Theoretical Expressivity of Graph Kernels

A Property Testing Framework for the Theoretical Expressivity of Graph Kernels

Abstract

Graph kernels are applied heavily for the classification of structured data. However, their expressivity is assessed almost exclusively from experimental studies and there is no theoretical justification why one kernel is in general preferable over another. We introduce a theoretical framework for investigating the expressive power of graph kernels, which is inspired by concepts from the area of property testing. We introduce the notion of distinguishability of a graph property by a graph kernel. For several established graph kernels we show that they cannot distinguish essential graph properties. In order to overcome this, we consider a kernel based on k-disc frequencies. We show that this efficiently computable kernel can distinguish fundamental graph properties. Finally, we obtain learning guarantees for nearest neighbor classifiers in our framework.

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Authors
  • Kriege, Nils M.
  • Morris, Christopher
  • Rey, Anja
  • Sohler, Christian
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Shortfacts
Category
Paper in Conference Proceedings or in Workshop Proceedings (Paper)
Event Title
27th International Joint Conference on Artificial Intelligence (IJCAI)
Divisions
Data Mining and Machine Learning
Event Location
Stockholm, Sweden
Event Type
Conference
Event Dates
13.07.2018
Series Name
Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence
ISSN/ISBN
978-0-9992411-2-7
Page Range
pp. 2348-2354
Date
13 July 2018
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