Network-based Neighborhood regression

2024-07-04

arXiv.org

AI Summary

Existing statistical analyses of biological modules often neglect network topology, failing to simultaneously capture global community structure and local connectivity patterns. To address this, we propose a neighborhood regression framework that jointly models community-level architecture and node-wise topological neighborhoods—marking the first such integration for module-level regulatory inference. Our method employs community-guided least-squares optimization, grounded in random graph theory and modular network embedding, yielding a non-asymptotic error bound. It achieves linear consistency (i.e., convergence rate O(1/n), not O(1/√n)) and non-asymptotic minimax optimality, thereby theoretically guaranteeing valid statistical inference at the module level. Applied to autism whole-exome sequencing and RNA-seq data, the framework successfully identifies statistically significant regulatory associations between genetically variant gene modules and differentially expressed gene modules—demonstrating both biological interpretability and practical utility.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Social Networks and Social Media: Computational social science
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Analyzes module-level regulation in biological networks using global and local connectivity.
• Develops a network-based neighborhood regression framework for optimal regulation strength estimation.
• Identifies associations between gene modules in genetic variations and differential expressions.

Innovation

• Network-based neighborhood regression framework
• Community-wise least square optimization
• Random graph theory for error bounds