Incremental Maintenance of Regression Models over Joins

This paper introduces a principled incremental view maintenance (IVM) mechanism for in-database computation described by rings. We exemplify our approach by introducing the covariance matrix ring that we use for learning linear regression models over arbitrary equi-join queries. Our approach is a higher-order IVM algorithm that exploits the factorized structure of joins and aggregates to avoid redundant computation and improve performance. We implemented it in DBToaster, which uses program synthesis to generate high-performance maintenance code. We experimentally show that it can outperform first-order and fully recursive higher-order IVM as well as recomputation by orders of magnitude while using less memory.