This article describes F-IVM, a unified approach for maintaining analytics over changing relational data. We exemplify its versatility in four disciplines: processing queries with group-by aggregates and joins; learning linear regression models using the covariance matrix of the input features; building Chow-Liu trees using pairwise mutual information of the input features; and matrix chain multiplication. F-IVM has three main ingredients: higher-order incremental view maintenance; factorized computation; and ring abstraction. F-IVM reduces the maintenance of a task to that of a hierarchy of simple views. Such views are functions mapping keys, which are tuples of input values, to payloads, which are elements from a ring. F-IVM also supports efficient factorized computation over keys, payloads, and updates. Finally, F-IVM treats uniformly seemingly disparate tasks. In the key space, all tasks require joins and variable marginalization. In the payload space, tasks differ in the definition of the sum and product ring operations. We implemented F-IVM on top of DBToaster and show that it can outperform classical first-order and fully recursive higher-order incremental view maintenance by orders of magnitude while using less memory.
翻译:F-IVM是维护对关系数据变化的分析的统一方法。我们用四个学科来展示它的多功能性:以集成和组合方式处理询问;使用输入特征的共变量矩阵学习线性回归模型;使用输入特征的双向信息建设周柳树;以及矩阵链乘法。F-IVM有三个主要要素:较高级递增视图维护;因数计算;和环抽象化。F-IVM将任务维持到简单观点的层次。这些观点是用于绘制键的功能,这是输入值图示,是来自环的元件。F-IVM还支持对键、有效载荷和更新进行高效的因数化计算。最后,F-IVM处理一致看似截然不同的任务。在关键空间,所有任务都需要组合和可变的边缘化。在有效载荷空间,任务在数量和产品环操作的定义上有所不同。我们在DBToster顶部执行F-IVM, 显示它能够使用较低的存储级先级,同时使用较慢的递增级的存储序列。</s>