Distributed Monitoring of the R2 Statistic for Linear Regression

This problem becomes challenging for large scale data in a distributed computing environment when only a subset of instances is available at individual nodes and the local data changes frequently. Data centralization and periodic model recomputation can add high overhead to tasks like anomaly detection in such dynamic settings.

Therefore, the goal is to develop techniques for monitoring and updating the model over the union of all nodes' data in a communication-efficient fashion. Correctness guarantees on such techniques are also often highly desirable, especially in safety-critical application scenarios. In this paper we develop DReMo --- a distributed algorithm with very low resource overhead, for monitoring the quality of a regression model in terms of its coefficient of determination ( R2 statistic).