  A central question in the era of 'big data' is what to do with the enormous
amount of information. One possibility is to characterize it through
statistics, e.g., averages, or classify it using machine learning, in order to
understand the general structure of the overall data. The perspective in this
paper is the opposite, namely that most of the value in the information in some
applications is in the parts that deviate from the average, that are unusual,
atypical. We define what we mean by 'atypical' in an axiomatic way as data that
can be encoded with fewer bits in itself rather than using the code for the
typical data. We show that this definition has good theoretical properties. We
then develop an implementation based on universal source coding, and apply this
to a number of real world data sets.
