  An ideal outcome of pattern mining is a small set of informative patterns,
containing no redundancy or noise, that identifies the key structure of the
data at hand. Standard frequent pattern miners do not achieve this goal, as due
to the pattern explosion typically very large numbers of highly redundant
patterns are returned.
  We pursue the ideal for sequential data, by employing a pattern set mining
approach-an approach where, instead of ranking patterns individually, we
consider results as a whole. Pattern set mining has been successfully applied
to transactional data, but has been surprisingly under studied for sequential
data.
  In this paper, we employ the MDL principle to identify the set of sequential
patterns that summarises the data best. In particular, we formalise how to
encode sequential data using sets of serial episodes, and use the encoded
length as a quality score. As search strategy, we propose two approaches: the
first algorithm selects a good pattern set from a large candidate set, while
the second is a parameter-free any-time algorithm that mines pattern sets
directly from the data. Experimentation on synthetic and real data demonstrates
we efficiently discover small sets of informative patterns.
