Distributed Sparse Regression via Penalization

We study sparse linear regression over a network of agents, modeled as an undirected graph (with no centralized node). The estimation problem is formulated as the minimization of the sum of the local LASSO loss functions plus a quadratic penalty of the consensus constraint—the latter being instrumental to obtain distributed solution methods. While penalty-based consensus methods have been extensively studied in the optimization literature, their statistical and computational guarantees in the high dimensional setting remain unclear. This work provides an …

agents consensus distributed functions graph lasso linear linear regression loss network node regression solution study