Distributed Monitoring of the R2 Statistic for Linear Regression
Kanishka Bhaduri, Kamalika Das, Chris R. Giannella · 2015
The problem of monitoring a multivariate linear regression model is relevant in studying the evolving relationship be-tween a set of input variables (features) and one or more de-pendent target variables. 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 centraliza-tion and periodic model recomputation can add high over-head to tasks like anomaly detection in such dynamic set-tings. Therefore, the goal is to develop techniques for mon-itoring and updating the model over the union of all nodes’ data in a communication-efficient fashion. Correctness guar-antees on such techniques are also often highly desirable, es-pecially 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 regres-sion model in terms of its coefficient of determination (R2 statistic). When the nodes collectively determine that R2 has dropped below a fixed threshold, the linear regression model is recomputed via a network-wide convergecast and the up-dated model is broadcast back to all nodes. We show empir-ically, using both synthetic and real data, that our proposed method is highly communication-efficient and scalable, and also provide theoretical guarantees on correctness. 1