Sparse Network Modeling

TL;DR

This paper discusses the challenges and methods for sparse network modeling in high-dimensional brain imaging data, highlighting computational bottlenecks and the scale limitations of current approaches.

Contribution

It provides an overview of sparse network models, their computational challenges, and the scale limitations in brain imaging applications.

Findings

Sparse models face computational bottlenecks due to L1-norm optimization.

Most models are limited to a few hundred nodes due to scalability issues.

The largest reported MRI feature set used in sparse modeling is 2527 features.

Abstract

There have been many attempts to identify high-dimensional network features via multivariate approaches. Specifically, when the number of voxels or nodes, denoted as p, are substantially larger than the number of images, denoted as n, it produces an under-determined model with infinitely many possible solutions. The small-n large-p problem is often remedied by regularizing the under-determined system with additional sparse penalties. Popular sparse network models include sparse correlations, LASSO, sparse canonical correlations and graphical-LASSO. These popular sparse models require optimizing L1-norm penalties, which has been the major computational bottleneck for solving large-scale problems. Thus, many existing sparse brain network models in brain imaging have been restricted to a few hundreds nodes or less. 2527 MRI features used in a LASSO model for Alzheimer's disease is probably the largest number of features used in any sparse model in the brain imaging literature.