When is Network Lasso Accurate?
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A main workhorse for statistical learning and signal processing using sparse models is the least absolute shrinkage and selection operator (Lasso). The Lasso has been adapted recently for massive network-structured datasets, i.e., big data over networks. In particular, the network Lasso allows to recover (or learn) graph signals from a small number of noisy signal samples by using the total variation semi-norm as a regularizer. Some work has been devoted to studying efficient and scalable implementations of the network Lasso. However, only little is known about the conditions on the underlying network structure which ensure a high accuracy of the network Lasso. 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 to deliver an accurate estimate of the entire underlying graph signal.
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