Pre and Post Counting for Scalable Statistical-Relational Model Discovery

TL;DR

This paper compares pre-counting and post-counting strategies for scalable statistical-relational model discovery, introducing a hybrid approach that balances memory and speed to handle large datasets effectively.

Contribution

It presents a novel hybrid counting method tailored for relational data, optimizing scalability by combining pre- and post-counting techniques.

Findings

Hybrid approach scales to millions of data facts.

Pre-counting benefits positive relationships.

Post-counting benefits negative relationships.

Abstract

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.