Analysis of Network Lasso for Semi-Supervised Regression

TL;DR

This paper analyzes the effectiveness of network Lasso in semi-supervised regression on network-structured data, linking its accuracy to network flow properties and providing conditions for reliable estimation.

Contribution

It offers a theoretical analysis of network Lasso's estimation error, connecting its accuracy to network flow conditions and the graph structure.

Findings

Network Lasso's accuracy depends on large network flows.

Conditions on network structure guarantee estimation accuracy.

Analysis links network Lasso to maximum flow problems.

Abstract

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.