Locally Consistent Bayesian Network Scores for Multi-Relational Data

An important task for relational learning is Bayesian network (BN) structure learning. A fundamental component of structure learning is a model selection score that measures how well a model fits a dataset. We describe a new method that upgrades for multi-relational databases, a log-linear BN score designed for single-table i.i.d. data. Chickering and Meek showed that for i.i.d. data, standard BN scores are locally consistent, meaning that their maxima converge to an optimal model, that represents the data generating distribution {\em and} contains no redundant edges. Our main theorem establishes that if a model selection score is locally consistent for i.i.d. data, then our upgraded gain function is locally consistent for relational data as well. To our knowledge this is the first consistency result for relational structure learning. A novel aspect of our approach is employing a {\em gain function} that compares two models: a current vs. an alternative BN structure. In contrast, previous approaches employed a score that is a function of a single model only. Empirical evaluation on six benchmark relational databases shows that our gain function is also practically useful: On realistic size data sets, it selects informative BN structures with a better data fit than those selected by baseline single-model scores.