The Logistic Network Lasso

TL;DR

This paper introduces the logistic network Lasso, a method that extends logistic regression to network-structured data by incorporating total variation regularization and scalable optimization techniques.

Contribution

It generalizes logistic regression to non-Euclidean network data using total variation regularization and develops a scalable algorithm based on ADMM.

Findings

Effective for binary classification on network data

Scalable implementation with inexact ADMM

Conforms to network structure via total variation

Abstract

We apply the network Lasso to solve binary classification and clustering problems for network-structured data. To this end, we generalize ordinary logistic regression to non-Euclidean data with an intrinsic network structure. The resulting "logistic network Lasso" amounts to solving a non-smooth convex regularized empirical risk minimization. The risk is measured using the logistic loss incurred over a small set of labeled nodes. For the regularization, we propose to use the total variation of the classifier requiring it to conform to the underlying network structure. A scalable implementation of the learning method is obtained using an inexact variant of the alternating direction methods of multipliers which results in a scalable learning algorithm