Finding the True Frequent Itemsets

Frequent Itemsets (FIs) mining is a fundamental primitive in data mining that requires to identify all itemsets appearing in a fraction at least θ of a transactional dataset D. Often though, the ultimate goal of mining D is not an analysis of the dataset per se, but the understanding of the underlying process that generated D. Specifically, in many applications D is a collection of samples obtained from an unknown probability distribution π on transactions, and by extracting the FIs in the dataset D one attempts to infer itemsets that are frequently generated by π, which we call the True Frequent Itemsets (TFIs). Due to the inherently random nature of the generative process, the set of FIs is only a rough approximation to the set of TFIs, as it often contains a huge number of spurious itemsets, i.e., itemsets that are not among the TFIs. In this work we present two methods to identify a collection of itemsets that contains only TFIs with probability at least 1 − δ (i.e., the methods have Family-Wise Error Rate bounded by δ), for some user-specified δ, without imposing any restriction on π. Our methods are distribution-free and make use of results from statistical learning theory involving the (empirical) VC-dimension of the problem at hand. This allows us to identify a larger fraction of the TFIs (i.e., to achieve higher statistical power) than what could be done using traditional multiple hypothesis testing corrections. In the experimental evaluation we compare our methods to established techniques (Bonferroni correction, holdout) and show that they return a very large subset of the TFIs, achieving a very high statistical power, while controlling the Family-Wise Error Rate.