This talk describes F-IVM, a unified approach for maintaining analytics over changing relational data. F-IVM can support diverse scenarios such as 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 general 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.

This talk is based on our SIGMOD 2018 and VLDB 2020 papers with new extensions currently under submissions.