Hyperrelations in version space

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A version space is a set of all hypotheses consistent with a given set of training examples, delimited by the specific boundary and the general boundary. In existing studies [4, 5, 3] a hypothesis is a conjunction of attribute-value pairs, which is shown to have limited expressive power [6]. In this paper we investigate version space in a more expressive hypothesis space, where a hypothesis is a hyper-relation, which is in effect a disjunction of conjunctions of disjunctions of attribute-value pairs. We propose to use an inductive bias, E-set, which turns our attention to equilabelled, supported, and maximal hypertuples. We characterise version space in such a hypothesis space under this bias and show the relationship between the specific boundary and general boundary with respect to unequivocal data, a special subset of the data space. We present experimental results on some public datasets.




Wang, H., Düntsch, I., Gediga, G., & Skowron, A. (2004). Hyperrelations in version space. International Journal of Approximate Reasoning, 36(3), 223–241. https://doi.org/10.1016/j.ijar.2003.10.007

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