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

Abstract

“I’m an MC still as honest” – Eminem, Rap God We present MCRapper, an algorithm for efficient computation of Monte-Carlo Empirical Rademacher Averages (MCERA) for families of functions exhibiting poset (e.g., lattice) structure, such as those that arise in many pattern mining tasks. The MCERA allows us to compute upper bounds to the maximum deviation of sample means from their expectations, thus it can be used to find both (1) statistically-significant functions (i.e., patterns) when the available data is seen as a sample from an unknown distribution, and (2) approximations of collections of high-expectation functions (e.g., frequent patterns) when the available data is a small sample from a large dataset. This flexibility offered by MCRapper is a big advantage over previously proposed solutions, which could only achieve one of the two. MCRapper uses upper bounds to the discrepancy of the functions to efficiently explore and prune the search space, a technique borrowed from pattern mining itself. To show the practical use of MCRapper, we employ it to develop an algorithm TFP-R for the task of True Frequent Pattern (TFP) mining, by appropriately computing approximations of the negative and positive borders of the collection of patterns of interest, which allow an effective pruning of the pattern space and the computation of strong bounds to the supremum deviation. TFP-R gives guarantees on the probability of including any false positives (precision) and exhibits higher statistical power (recall) than existing methods offering the same guarantees. We evaluate MCRapper and TFP-R and show that they outperform the state-of-the-art for their respective tasks.