In-Network Linear Regression with Arbitrarily Split Data Matrices

TL;DR

This paper proposes a distributed optimization framework enabling a network of agents to collaboratively perform linear regression despite each agent having only a partial and arbitrarily split subset of the data matrix.

Contribution

It introduces a variable-centric framework and a proximal algorithm based on Douglas-Rachford splitting for in-network linear regression with arbitrary data splits.

Findings

Developed a novel distributed optimization algorithm

Handled arbitrary data splits among agents

Demonstrated convergence of the proposed method

Abstract

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.