  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.
