# Localized Linear Regression in Networked Data

arXiv: https://arxiv.org/abs/1903.11178 · HTML: https://mlsanity.com/paper/1903.11178/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Mar 2019.

## Built on by (most cited first, 8 of 8)

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- [LogSpecT: Feasible Graph Learning Model from Stationary Signals with Recovery Guarantees](https://mlsanity.com/paper/2305.01379/) (2023)
- [Analysis of Total Variation Minimization for Clustered Federated Learning](https://mlsanity.com/paper/2403.06298/) (2024)
- [Hierarchical Clustering and Signal Denoising on Digraphs](https://mlsanity.com/paper/2609.34670/) (2026)

## Abstract (arXiv)

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.