Analysis of Network Lasso for Semi-Supervised Regression
This work addresses semi-supervised regression for network data, offering theoretical insights but is incremental as it analyzes an existing method.
The paper tackles the problem of analyzing the estimation error of network Lasso for semi-supervised regression on network-structured data, revealing that its accuracy depends on conditions like network flows and training data, with guarantees provided under these conditions.
We apply network Lasso to semi-supervised regression problems involving network structured data. This approach lends quite naturally to highly scalable learning algorithms in the form of message passing over an empirical graph which represents the network structure of the data. By using a simple non-parametric regression model, which is motivated by a clustering hypothesis, we provide an analysis of the estimation error incurred by network Lasso. This analysis reveals conditions on the the network structure and the available training data which guarantee network Lasso to be accurate. Remarkably, the accuracy of network Lasso is related to the existence of sufficiently large network flows over the empirical graph. Thus, our analysis reveals a connection between network Lasso and maximum flow problems.