# Classifying Partially Labeled Networked Data via Logistic Network Lasso

## TL;DR

This paper introduces a scalable method using the logistic network Lasso for classifying high-dimensional, partially labeled networked data by leveraging the network structure to improve accuracy with limited labels.

## Contribution

It presents a novel regularized empirical risk minimization framework employing total variation and a primal-dual splitting method for efficient large-scale classification.

## Key findings

- Effective classification with limited labels
- Scalable message passing implementation
- Improved accuracy leveraging network structure

## Abstract

We apply the network Lasso to classify partially labeled data points which are characterized by high-dimensional feature vectors. In order to learn an accurate classifier from limited amounts of labeled data, we borrow statistical strength, via an intrinsic network structure, across the dataset. The resulting logistic network Lasso amounts to a regularized empirical risk minimization problem using the total variation of a classifier as a regularizer. This minimization problem is a non-smooth convex optimization problem which we solve using a primal-dual splitting method. This method is appealing for big data applications as it can be implemented as a highly scalable message passing algorithm.