Symmetric Bilinear Regression for Signal Subgraph Estimation

TL;DR

This paper introduces a symmetric bilinear regression model with L1 penalty for identifying small, outcome-relevant subgraphs in large brain networks, improving interpretability and prediction of cognitive traits.

Contribution

It proposes a novel symmetric bilinear model with L1 regularization and a coordinate descent algorithm for efficient subgraph detection in high-dimensional brain networks.

Findings

Identified relevant interconnections among brain regions related to cognition.

Achieved better predictive performance than existing methods.

Discovered small subgraphs linked to human cognitive traits.

Abstract

There is increasing interest in learning a set of small outcome-relevant subgraphs in network-predictor regression. The extracted signal subgraphs can greatly improve the interpretation of the association between the network predictor and the response. In brain connectomics, the brain network for an individual corresponds to a set of interconnections among brain regions and there is a strong interest in linking the brain connectome to human cognitive traits. Modern neuroimaging technology allows a very fine segmentation of the brain, producing very large structural brain networks. Therefore, accurate and efficient methods for identifying a set of small predictive subgraphs become crucial, leading to discovery of key interconnected brain regions related to the trait and important insights on the mechanism of variation in human cognitive traits. We propose a symmetric bilinear model with $L_1$ penalty to search for small clique subgraphs that contain useful information about the response. A coordinate descent algorithm is developed to estimate the model where we derive analytical solutions for a sequence of conditional convex optimizations. Application of this method on human connectome and language comprehension data shows interesting discovery of relevant interconnections among several small sets of brain regions and better predictive performance than competitors.