# Localized Linear Regression in Networked Data

## TL;DR

This paper analyzes the statistical properties of the network Lasso (nLasso) for localized linear regression on networked data, providing conditions for accurate learning from limited labels and an implementation via primal-dual methods.

## Contribution

It offers a theoretical analysis of nLasso's ability to learn localized linear models with few labels and presents a specialized implementation using primal-dual optimization.

## Key findings

- Identifies sufficient conditions on network structure and labels for accurate nLasso learning.
- Provides a scalable primal-dual algorithm for localized linear regression with nLasso.
- Demonstrates the effectiveness of nLasso in networked data scenarios.

## Abstract

The network Lasso (nLasso) has been proposed recently as an efficient learning algorithm for massive networked data sets (big data over networks). It extends the well-known least absolute shrinkage and selection operator (Lasso) from learning sparse (generalized) linear models to network models. Efficient implementations of the nLasso have been obtained using convex optimization methods lending to scalable message passing protocols. In this paper, we analyze the statistical properties of nLasso when applied to localized linear regression problems involving networked data. Our main result is a sufficient condition on the network structure and available label information such that nLasso accurately learns a localized linear regression model from a few labeled data points. We also provide an implementation of nLasso for localized linear regression by specializing a primaldual method for solving the convex (non-smooth) nLasso problem.