Integrated solutions for analytics over relational databases are of great practical importance as they avoid the costly repeated loop data scientists have to deal with on a daily basis: select features from data residing in relational databases using feature extraction queries involving joins, projections, and aggregations; export the training dataset defined by such queries; convert this dataset into the format of an external learning tool; and train the desired model using this tool. These integrated solutions are also a fertile ground of theoretically fundamental and challenging problems at the intersection of relational and statistical data models. This article introduces a unified framework for training and evaluating a class of statistical learning models over relational databases. This class includes ridge linear regression, polynomial regression, factorization machines, and principal component analysis. We show that, by synergizing key tools from database theory such as schema information, query structure, functional dependencies, recent advances in query evaluation algorithms, and from linear algebra such as tensor and matrix operations, one can formulate relational analytics problems and design efficient (query and data) structure-aware algorithms to solve them. This theoretical development informed the design and implementation of the AC/DC system for structure-aware learning. We benchmark the performance of AC/DC against R, MADlib, libFM, and TensorFlow. For typical retail forecasting and advertisement planning applications, AC/DC can learn polynomial regression models and factorization machines with at least the same accuracy as its competitors and up to three orders of magnitude faster than its competitors whenever they do not run out of memory, exceed 24-hour timeout, or encounter internal design limitations.

中文翻译：

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使用稀疏张量和函数依赖关系学习模型

对关系数据库进行分析的集成解决方案具有非常重要的实际意义，因为它们避免了数据科学家每天必须处理的代价高昂的重复循环：使用涉及连接、投影和聚合的特征提取查询从关系数据库中的数据中选择特征；导出此类查询定义的训练数据集；将此数据集转换为外部学习工具的格式；并使用此工具训练所需的模型。这些集成解决方案也是关系数据模型和统计数据模型交叉领域的理论基础和挑战性问题的沃土。本文介绍了一个统一的框架，用于在关系数据库上训练和评估一类统计学习模型。这个类包括岭线性回归，多项式回归、分解机和主成分分析。我们表明，通过协同来自数据库理论的关键工具，如模式信息、查询结构、函数依赖关系、查询评估算法的最新进展，以及来自线性代数（如张量和矩阵运算）的关键工具，可以制定关系分析问题并提高设计效率。查询和数据）结构感知算法来解决它们。这一理论发展为结构感知学习的 AC/DC 系统的设计和实施提供了信息。我们针对 R、MADlib、libFM 和 TensorFlow 对 AC/DC 的性能进行了基准测试。对于典型的零售预测和广告策划应用，