Abstract
We introduce a general definition for the independence of a number of finite-valued variables, based on coherent lower previsions. Our definition has an epistemic flavour: it arises from personal judgements that a number of variables are irrelevant to one another. We show that a number of already existing notions, such as strong independence, satisfy our definition. Moreover, there always is a least-committal independent model, for which we provide an explicit formula: the independent natural extension. Our central result is that the independent natural extension satisfies so-called marginalisation, associativity and strong factorisation properties. These allow us to relate our research to more traditional ways of defining independence based on factorisation.
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de Cooman, G., Miranda, E., Zaffalon, M. (2010). Independent Natural Extension. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Computational Intelligence for Knowledge-Based Systems Design. IPMU 2010. Lecture Notes in Computer Science(), vol 6178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14049-5_75
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DOI: https://doi.org/10.1007/978-3-642-14049-5_75
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14048-8
Online ISBN: 978-3-642-14049-5
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