Maximum entropy models and subjective interestingness: an application to tiles in binary databases
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, Proceedings of the 1st ACM SIGKDD international conference on Knowledge discovery and data mining (KDD95), 1995; Geng and Hamilton, ACM Comput Surv 38(3):9, 2006). A key challenge here is the formalization of this prior information in a way that lends itself to the definition of a subjective interestingness 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 variousmeasures 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 rowand column sums. This situation has been considered before using computation intensive approaches based on swap randomizations, allowing for the computation of empirical p-values as interestingnessmeasures (Gionis et al.,ACM Trans Knowl Discov Data 1(3):14, 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, theMaxEntmodel can additionally be used to deﬁne analytically computable interestingnessmeasures, aswe demonstrate for tiles (Geerts et al., Proceedings of the 7th international conference on Discovery science (DS04), 2004) in binary databases.