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In this paper, we address the problem of how a network of agents cancollaboratively fit a linear model when each agent only ever has an arbitrarysummand of the regression data. This problem generalizes previously studieddata-matrix-splitting scenarios, allowing for some agents to have moremeasurements of some features than of others and even have measurements thatother agents have. We present a variable-centric framework for distributedoptimization in a network, and use this framework to develop a proximalalgorithm, based on the Douglas-Rachford method, that solves the problem.

In-Network Linear Regression with Arbitrarily Split Data Matrices