  Recent sequential pattern mining methods have used the minimum description
length (MDL) principle to define an encoding scheme which describes an
algorithm for mining the most compressing patterns in a database. We present a
novel subsequence interleaving model based on a probabilistic model of the
sequence database, which allows us to search for the most compressing set of
patterns without designing a specific encoding scheme. Our proposed algorithm
is able to efficiently mine the most relevant sequential patterns and rank them
using an associated measure of interestingness. The efficient inference in our
model is a direct result of our use of a structural expectation-maximization
framework, in which the expectation-step takes the form of a submodular
optimization problem subject to a coverage constraint. We show on both
synthetic and real world datasets that our model mines a set of sequential
patterns with low spuriousness and redundancy, high interpretability and
usefulness in real-world applications. Furthermore, we demonstrate that the
quality of the patterns from our approach is comparable to, if not better than,
existing state of the art sequential pattern mining algorithms.
