Declarative Parameterizations of User-Defined Functions for Large-Scale Machine Learning and Optimization

Large-scale optimization has become an important application for data management systems, particularly in the context of statistical machine learning. In this paper, we consider how one might implement the join-and-co-group pattern in the context of a fully declarative data processing system. The join-and-co-group pattern is ubiquitous in iterative, large-scale optimization. In the join-and-co-group pattern, a user-defined function $g$g is parameterized with a data object $x$x as well as the subset of the statistical model $\Theta _x$Θx that applies to that object, so that $g(x | \Theta _x)$g(x|Θx) can be used to compute a partial update of the model. This is repeated for every $x$x in the full data set $X$X. All partial updates are then aggregated and used to perform a complete update of the model. The join-and-co-group pattern has several implementation challenges, including the potential for a massive blow-up in the size of a fully parameterized model. Thus, unless the correct physical execution plan be chosen for implementing the join-and-co-group pattern, it is easily possible to have an execution that takes a very long time or even fails to complete. In this paper, we carefully consider the alternatives for implementing the join-and-co-group pattern on top of a declarative system, as well as how the best alternative can be selected automatically. Our focus is on the SimSQL database system, which is an SQL-based system with special facilities for large-scale, iterative optimization. Since it is an SQL-based system with a query optimizer, those choices can be made automatically.