When is Network Lasso Accurate?

The network Lasso is a recently proposed method for clustering and optimization problems arising from massive network structured datasets, i.e., big data over networks. It is a variant of the well-known least absolute shrinkage and selection operator (Lasso), which is underlying many methods in learning and signal processing involving sparse models. While some work has been devoted to studying efficient and scalable implementations of the network Lasso, only little is known about conditions on the underlying network structure required by network Lasso to be accurate. We address this gap by giving precise conditions on the underlying network topology which guarantee the network lasso to be accurate.