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Recent research has highlighted the practical benefits of subjective interestingness measures, which quantify the novelty or unexpectedness of a pattern when contrasted with any prior information of the data miner (Silberschatz and Tuzhilin, 1995; Geng and Hamilton, 2006). A key challenge here is the formalization of this prior information in a way that lends itself to the definition of an interestingness subjective measure that is both meaningful and practical. In this paper, we outline a general strategy of how this could be achieved, before working out the details for a use case that is important in its own right. Our general strategy is based on considering prior information as constraints on a probabilistic model representing the uncertainty about the data. More specifically, we represent the prior information by the maximum entropy (MaxEnt) distribution subject to these constraints. We briefly outline various measures that could subsequently be used to contrast patterns with this MaxEnt model, thus quantifying their subjective interestingness. We demonstrate this strategy for rectangular databases with knowledge of the row and column sums. This situation has been considered before using computation intensive approaches based on swap randomizations, allowing for the computation of empirical pvalues as interestingness measures (Gionis et al, 2007). We show how the MaxEnt model can be computed remarkably efficiently in this situation, and how it can be used for the same purpose as swap randomizations but computationally more efficiently. More importantly, being an explicitly represented distribution, the MaxEnt model can additionally be used to define analytically computable interestingness measures, as we demonstrate for tiles (Geerts et al, 2004) in binary databases.
|Translated title of the contribution||Maximum entropy models and subjective interestingness: an application to tiles in binary databases|
|Number of pages||43|
|Journal||Data Mining and Knowledge Discovery|
|Publication status||Published - Nov 2011|
Bibliographical notePublisher: University of Bristol
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