We investigate the problem of building least squares regression models over training datasets defined by arbitrary join queries on database tables. Our key observation is that joins entail a high degree of redundancy in both computation and data representation, which is not required for the end-to-end solution to learning over joins.We propose a new paradigm for computing batch gradient descent that exploits the factorized computation and representation of the training datasets, a rewriting of the regression objective function that decouples the computation of cofactors of model parameters from their convergence, and the commutativity of cofactor computation with relational union and projection. We introduce three flavors of this approach: F/FDB computes the cofactors in one pass over the materialized factorized join; F avoids this materialization and intermixes cofactor and join computation; F/SQL expresses this mixture as one SQL query.Our approach has the complexity of join factorization, which can be exponentially lower than of standard joins. Experiments with commercial, public, and synthetic datasets show that it outperforms MADlib, Python StatsModels, and R, by up to three orders of magnitude.

In-database analytics is of great practical importance as it avoids the costly repeated loop data scientists have to deal with on a daily basis: select features, export the data, convert data format, train models using an external tool, reimport the parameters. It is also a fertile ground of theoretically fundamental and challenging problems at the intersection of relational and statistical data models.This paper introduces a unified framework for training and evaluating a class of statistical learning models inside a relational database. This class includes ridge linear regression, polynomial regression, factorization machines, and principal component analysis. We show that, by synergizing key tools from relational database theory such as schema information, query structure, recent advances in query evaluation algorithms, and from linear algebra such as various tensor and matrix operations, one can formulate in-database learning problems and design efficient algorithms to solve them.The algorithms and models proposed in the paper have already been implemented and deployed in retail-planning and forecasting applications, with significant performance benefits over out-ofdatabase solutions that require the costly data-export loop.

Motivated by fundamental applications in databases and relational machine learning, we formulate and study the problem of answering functional aggregate queries (FAQ) in which some of the input factors are defined by a collection of additive inequalities between variables. We refer to these queries as FAQ-AI for short. To answer FAQ-AI in the Boolean semiring, we define relaxed tree decompositions and relaxed submodular and fractional hypertree width parameters. We show that an extension of the InsideOut algorithm using Chazelle’s geometric data structure for solving the semigroup range search problem can answer Boolean FAQ-AI in time given by these new width parameters. This new algorithm achieves lower complexity than known solutions for FAQ-AI. It also recovers some known results in database query answering. Our second contribution is a relaxation of the set of polymatroids that gives rise to the counting version of the submodular width, denoted by #subw. This new width is sandwiched between the submodular and the fractional hypertree widths. Any FAQ and FAQ-AI over one semiring can be answered in time proportional to #subw and respectively to the relaxed version of #subw. We present three applications of our FAQ-AI framework to relational machine learning: k -means clustering, training linear support vector machines, and training models using non-polynomial loss. These optimization problems can be solved over a database asymptotically faster than computing the join of the database relations.

This paper overviews factorized databases and their application to machine learning. The key observation underlying this work is that state-of-the-art relational query processing entails a high degree of redundancy in the computation and representation of query results. This redundancy can be avoided and is not necessary for subsequent analytics such as learning regression models.

is paper introduces LMFAO (Layered Multiple Functional Aggregate Optimization), an in-memory optimization and execution engine for batches of aggregates over the input database. e primary motivation for this work stems from the observation that for a variety of analytics over databases, their data-intensive tasks can be decomposed into groupby aggregates over the join of the input database relations. We exemplify the versatility and competitiveness of LMFAO for a handful of widely used analytics: learning ridge linear regression, classi cation trees, regression trees, and the structure of Bayesian networks using Chow-Liu trees; and data cubes used for exploration in data warehousing.LMFAO consists of several layers of logical and code optimizations that systematically exploit sharing of computation, parallelism, and code specialization.We conducted two types of performance benchmarks. In experiments with four datasets, LMFAO outperforms by several orders of magnitude on one hand, a commercial database system and MonetDB for computing batches of aggregates, and on the other hand, TensorFlow, Scikit, R, and AC/DC for learning a variety of models over databases.