In-Network Linear Regression with Arbitrarily Split Data Matrices

In this paper, we address the problem of how a network of agents can collaboratively fit a linear model when each agent only ever has an arbitrary summand of the regression data. This problem generalizes previously studied data-matrix-splitting scenarios, allowing for some agents to have more measurements of some features than of others and even have measurements that other agents have. We present a variable-centric framework for distributed optimization in a network, and use this framework to develop a proximal algorithm, based on the Douglas-Rachford method, that solves the problem.