When is Network Lasso Accurate?
This addresses a gap in understanding for researchers using network Lasso in graph signal processing, providing theoretical guarantees for accuracy.
The paper tackles the problem of determining when network Lasso accurately learns graph signals from noisy samples, deriving precise conditions on network topology and sampling sets that guarantee accurate estimates and quantifying error in terms of connectivity constants.
The "least absolute shrinkage and selection operator" (Lasso) method has been adapted recently for networkstructured 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.