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We present MCRapper, an algorithm for efficient computation of Monte-CarloEmpirical Rademacher Averages (MCERA) for families of functions exhibitingposet (e.g., lattice) structure, such as those that arise in many patternmining tasks. The MCERA allows us to compute upper bounds to the maximumdeviation of sample means from their expectations, thus it can be used to findboth statistically-significant functions (i.e., patterns) when the availabledata is seen as a sample from an unknown distribution, and approximations ofcollections of high-expectation functions (e.g., frequent patterns) when theavailable data is a small sample from a large dataset. This feature is a strongimprovement over previously proposed solutions that could only achieve one ofthe two. MCRapper uses upper bounds to the discrepancy of the functions toefficiently explore and prune the search space, a technique borrowed frompattern mining itself. To show the practical use of MCRapper, we employ it todevelop an algorithm TFP-R for the task of True Frequent Pattern (TFP) mining.TFP-R gives guarantees on the probability of including any false positives(precision) and exhibits higher statistical power (recall) than existingmethods offering the same guarantees. We evaluate MCRapper and TFP-R and showthat they outperform the state-of-the-art for their respective tasks.

MCRapper: Monte-Carlo Rademacher Averages for Poset Families and Approximate Pattern Mining