  One of the main current challenges in itemset mining is to discover a small
set of high-quality itemsets. In this paper we propose a new and general
approach for measuring the quality of itemsets. The method is solidly founded
in Bayesian statistics and decreases monotonically, allowing for efficient
discovery of all interesting itemsets. The measure is defined by connecting
statistical models and collections of itemsets. This allows us to score
individual itemsets with the probability of them occuring in random models
built on the data.
  As a concrete example of this framework we use exponential models. This class
of models possesses many desirable properties. Most importantly, Occam's razor
in Bayesian model selection provides a defence for the pattern explosion. As
general exponential models are infeasible in practice, we use decomposable
models; a large sub-class for which the measure is solvable. For the actual
computation of the score we sample models from the posterior distribution using
an MCMC approach.
  Experimentation on our method demonstrates the measure works in practice and
results in interpretable and insightful itemsets for both synthetic and
real-world data.
