  Statistical-Relational Model Discovery aims to find statistically relevant
patterns in relational data. For example, a relational dependency pattern may
stipulate that a user's gender is associated with the gender of their friends.
As with propositional (non-relational) graphical models, the major scalability
bottleneck for model discovery is computing instantiation counts: the number of
times a relational pattern is instantiated in a database. Previous work on
propositional learning utilized pre-counting or post-counting to solve this
task. This paper takes a detailed look at the memory and speed trade-offs
between pre-counting and post-counting strategies for relational learning. A
pre-counting approach computes and caches instantiation counts for a large set
of relational patterns before model search. A post-counting approach computes
an instantiation count dynamically on-demand for each candidate pattern
generated during the model search. We describe a novel hybrid approach,
tailored to relational data, that achieves a sweet spot with pre-counting for
patterns involving positive relationships (e.g. pairs of users who are friends)
and post-counting for patterns involving negative relationships (e.g. pairs of
users who are not friends). Our hybrid approach scales model discovery to
millions of data facts.
