06110592

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06110592 H\"ullermeier, Eyke Tehrani, Ali Fallah On the VC-dimension of the Choquet integral. Greco, Salvatore (ed.) et al., Advances in computational intelligence. 14th international conference on information processing and management of uncertainty in knowledge-based systems, IPMU 2012, Catania, Italy, July 9--13, 2012. Proceedings, Part I. Berlin: Springer (ISBN 978-3-642-31708-8/pbk; 978-3-642-31709-5/ebook). Communications in Computer and Information Science 297, 42-50 (2012). 2012 Berlin: Springer EN

doi:10.1007/978-3-642-31709-5_5

Summary: The idea of using the Choquet integral as an aggregation operator in machine learning has gained increasing attention in recent years, and a number of corresponding methods have already been proposed. Complementing these contributions from a more theoretical perspective, this paper addresses the following question: What is the VC dimension of the (discrete) Choquet integral when being used as a binary classifier? The VC dimension is a key notion in statistical learning theory and plays an important role in estimating the generalization performance of a learning method. Although we cannot answer the above question exactly, we provide a first interesting result in the form of (relatively tight) lower and upper bounds.