Enabling and Optimizing Non-linear Feature Interactions in Factorized Linear Algebra

Accelerating machine learning (ML) over relational data is a key focus of the database community. While many real-world datasets are multi-table, most ML tools expect single-table inputs, forcing users to materialize joins before ML, leading to data redundancy and runtime waste. Recent works on ''factorized ML'' address such issues by pushing ML through joins. However, they have hitherto been restricted to ML models linear in the feature space, rendering them less effective when users construct non-linear feature interactions such as pairwise products to boost ML accuracy. In this work, we take a first step towards closing this gap by introducing a new abstraction to enable pairwise feature interactions in multi-table data and present an extensive framework of algebraic rewrite rules for factorized LA operators over feature interactions. Our rewrite rules carefully exploit the interplay of the redundancy caused by both joins and interactions. We prototype our framework in Python to build a tool we call MorpheusFI. An extensive empirical evaluation with both synthetic and real datasets shows that MorpheusFI yields up to 5x speedups over materialized execution for a popular second-order gradient method and even an order of magnitude speedups over a popular stochastic gradient method.