Network-based Neighborhood regression

TL;DR

This paper introduces a novel network-based neighborhood regression framework that integrates global community information and local connectivity to analyze biological modules, providing optimal estimation bounds and demonstrating effectiveness on genetic datasets.

Contribution

The paper presents a new regression framework that leverages network structures for biological module analysis, with an efficient optimization method and theoretical guarantees.

Findings

Achieves exact minimax optimality in estimation error bounds.

Demonstrates linear consistency in the number of nodes n.

Effectively identifies gene module associations in genetic datasets.

Abstract

Given the ubiquity of modularity in biological systems, module-level regulation analysis is vital for understanding biological systems across various levels and their dynamics. Current statistical analysis on biological modules predominantly focuses on either detecting the functional modules in biological networks or sub-group regression on the biological features without using the network data. This paper proposes a novel network-based neighborhood regression framework whose regression functions depend on both the global community-level information and local connectivity structures among entities. An efficient community-wise least square optimization approach is developed to uncover the strength of regulation among the network modules while enabling asymptotic inference. With random graph theory, we derive non-asymptotic estimation error bounds for the proposed estimator, achieving exact minimax optimality. Unlike the root-n consistency typical in canonical linear regression, our model exhibits linear consistency in the number of nodes n, highlighting the advantage of incorporating neighborhood information. The effectiveness of the proposed framework is further supported by extensive numerical experiments. Application to whole-exome sequencing and RNA-sequencing Autism datasets demonstrates the usage of the proposed method in identifying the association between the gene modules of genetic variations and the gene modules of genomic differential expressions.