Alice and the Caterpillar: A more descriptive null model for assessing data mining results

TL;DR

This paper introduces advanced null models for binary transactional and sequence datasets that preserve more properties, enabling more accurate statistical hypothesis testing and revealing new significant results.

Contribution

The paper presents Alice, a suite of MCMC algorithms for sampling from null models that maintain complex dataset properties, improving assessment of data mining results.

Findings

Alice mixes rapidly and scales well

Null models reveal different significant results

Preserve properties like the bipartite joint degree matrix

Abstract

We introduce novel null models for assessing the results obtained from observed binary transactional and sequence datasets, using statistical hypothesis testing. Our null models maintain more properties of the observed dataset than existing ones. Specifically, they preserve the Bipartite Joint Degree Matrix of the bipartite (multi-)graph corresponding to the dataset, which ensures that the number of caterpillars, i.e., paths of length three, is preserved, in addition to other properties considered by other models. We describe Alice, a suite of Markov chain Monte Carlo algorithms for sampling datasets from our null models, 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.