When is Network Lasso Accurate: The Vector Case

TL;DR

This paper analyzes the conditions under which the network Lasso algorithm accurately learns vector-valued signals on large networks, extending sparse modeling techniques to network-structured data.

Contribution

It provides sufficient conditions on network structure and label information for accurate learning with the network Lasso, advancing understanding of its effectiveness.

Findings

Identifies network conditions for nLasso accuracy

Extends Lasso to vector-valued graph signals

Provides theoretical guarantees for label-based learning

Abstract

A recently proposed learning algorithm for massive network-structured data sets (big data over networks) is the network Lasso (nLasso), which extends the well- known Lasso estimator from sparse models to network-structured datasets. Efficient implementations of the nLasso have been presented using modern convex optimization methods. In this paper, we provide sufficient conditions on the network structure and available label information such that nLasso accurately learns a vector-valued graph signal (representing label information) from the information provided by the labels of a few data points.