Alice and the Caterpillar: A More Descriptive Null Model for Assessing Data Mining Results

Abstract

“One side will make you grow taller, and the other side will make you grow shorter – The Caterpillar, Alice in Wonderland We introduce a novel null model for assessing the results obtained by analyzing an observed transactional dataset (e.g., significant frequent itemsets) using statistical hypothesis testing. Our null model maintains more properties of the observed dataset than existing models. Specifically, we preserve the Bipartite Joint Degree Matrix of the bipartite graph corresponding to the dataset, which ensures that the number of caterpillars, i.e., paths of length three, is preserved, in addition to the item supports and the transaction lengths, which are the properties considered by previous works. We describe ALICE, a suite of two Markov-Chain Monte-Carlo algorithms for sampling datasets from our null model, based on a carefully defined set of states and efficient operations to move between them. The results of our experimental evaluation show that ALICE mixes fast and scales well, and that our null model finds different significant results than ones previously considered in the literature.