Connections between Mining Frequent Itemsets and Learning Generative Models

Frequent itemsets mining is a popular framework for pattern discovery. In this framework, given a database of customer transactions, the task is to unearth all patterns in the form of sets of items appearing in a sizable number of transactions. We present a class of models called Itemset Generating Models (or IGMs) that can be used to formally connect the process of frequent item- sets discovery with the learning of generative models. IGMs are specified using simple probability mass functions (over the space of transactions), peaked at specific sets of items and uniform everywhere else. Under such a connection, it is possible to rigorously associate higher frequency patterns with generative models that have greater data likelihoods. This enables a generative model-learning interpretation of frequent itemsets mining. More importantly, it facilitates a statistical significance test which prescribes the minimum frequency needed for a pattern to be considered interesting. We illustrate the effectiveness of our analysis through experiments on standard benchmark data sets.