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Attribute interactions are the irreducible dependencies between attributes. Interactions underlie feature relevance and selection, the structure of joint probability and classification models: if and only if the attributes interact, they should be connected. While the issue of 2-way interactions, especially of those between an attribute and the label, has already been addressed, we introduce an operational definition of a generalized n-way interaction by highlighting two models: the reductionistic part-to-whole approximation, where the model of the whole is reconstructed from models of the parts, and the holistic reference model, where the whole is modelled directly. An interaction is deemed significant if these two models are significantly different. In this paper, we propose the Kirkwood superposition approximation for constructing part-to-whole approximations. To model data, we do not assume a particular structure of …