A Convex Formulation for Learning Scale-Free Networks via Submodular Relaxation

TL;DR

This paper introduces a convex optimization approach using submodular relaxation to learn scale-free networks, improving accuracy in synthetic data and encouraging scale-free structures in biological data.

Contribution

It proposes a novel convex formulation for learning scale-free networks using submodular functions and Lovász extension, enabling efficient optimization.

Findings

Improved network reconstruction accuracy on synthetic data

Encourages scale-free structures in biological datasets

Efficient convex optimization method

Abstract

A key problem in statistics and machine learning is the determination of network structure from data. We consider the case where the structure of the graph to be reconstructed is known to be scale-free. We show that in such cases it is natural to formulate structured sparsity inducing priors using submodular functions, and we use their Lov\'asz extension to obtain a convex relaxation. For tractable classes such as Gaussian graphical models, this leads to a convex optimization problem that can be efficiently solved. We show that our method results in an improvement in the accuracy of reconstructed networks for synthetic data. We also show how our prior encourages scale-free reconstructions on a bioinfomatics dataset.