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Large sparse sets of binary transaction data with millions of records andthousands of attributes occur in various domains: customers purchasingproducts, users visiting web pages, and documents containing words are justthree typical examples. Real-time query selectivity estimation (the problem ofestimating the number of rows in the data satisfying a given predicate) is animportant practical problem for such databases.  We investigate the application of probabilistic models to this problem. Inparticular, we study a Markov random field (MRF) approach based on frequentsets and maximum entropy, and compare it to the independence model and theChow-Liu tree model. We find that the MRF model provides substantially moreaccurate probability estimates than the other methods but is more expensivefrom a computational and memory viewpoint. To alleviate the computationalrequirements we show how one can apply bucket elimination and clique treeapproaches to take advantage of structure in the models and in the queries. Weprovide experimental results on two large real-world transaction datasets.

Probabilistic Models for Query Approximation with Large Sparse Binary Datasets