Independent natural extension

Authors:
Gert De Cooman;Enrique Miranda;Marco Zaffalon
Affiliations:
SYSTeMS, Ghent University, Belgium;University of Oviedo, Spain;IDSIA, Manno, Lugano, Switzerland
Venue:
IPMU'10 Proceedings of the Computational intelligence for knowledge-based systems design, and 13th international conference on Information processing and management of uncertainty
Year:
2010

Citing 3
Cited 3

A survey of the theory of coherent lower previsions

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Updating coherent previsions on finite spaces

Fuzzy Sets and Systems
Epistemic irrelevance in credal nets: The case of imprecise Markov trees

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Probability boxes on totally preordered spaces for multivariate modelling

International Journal of Approximate Reasoning
Independent natural extension

Artificial Intelligence
Independence and 2-monotonicity: nice to have, hard to keep

ECSQARU'11 Proceedings of the 11th European conference on Symbolic and quantitative approaches to reasoning with uncertainty

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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.