AUTHOR=Jung Alexander , Tran Nguyen , Mara Alexandru TITLE=When Is Network Lasso Accurate? JOURNAL=Frontiers in Applied Mathematics and Statistics VOLUME=3 YEAR=2018 URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2017.00028 DOI=10.3389/fams.2017.00028 ISSN=2297-4687 ABSTRACT=

The “least absolute shrinkage and selection operator” (Lasso) method has been adapted recently for network-structured datasets. In particular, this network Lasso method allows to learn graph signals from a small number of noisy signal samples by using the total variation of a graph signal for regularization. While efficient and scalable implementations of the network Lasso are available, only little is known about the conditions on the underlying network structure which ensure network Lasso to be accurate. By leveraging concepts of compressed sensing, we address this gap and derive precise conditions on the underlying network topology and sampling set which guarantee the network Lasso for a particular loss function to deliver an accurate estimate of the entire underlying graph signal. We also quantify the error incurred by network Lasso in terms of two constants which reflect the connectivity of the sampled nodes.