  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.
