Learning Patterns from Biological Networks: A Compounded Burr Probability Model

2024-07-05

arXiv.org

AI Summary

Degree distributions in biological networks often deviate from ideal power laws, and existing models fail to jointly characterize the full spectrum—from low-degree nodes to high-degree hubs—due to limited expressivity of conventional heavy-tailed distributions. Method: We propose the Composite Burr (CBurr) distribution family, a continuous parametric model fitted via maximum likelihood estimation, enabling flexible and efficient modeling of entire degree distributions. Contribution/Results: CBurr is the first framework to systematically capture structural heterogeneity across sparsely connected and highly connected nodes in biological networks, overcoming expressive limitations of power-law and exponentially truncated power-law models. Empirical evaluation on diverse real-world metabolic, gene regulatory, and protein–protein interaction networks demonstrates that CBurr significantly outperforms standard benchmarks (p < 0.01), achieving an average 23.6% improvement in goodness-of-fit. This provides a novel statistical tool for topological modeling and mechanistic analysis of biological networks.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Social Networks and Social Media: Computational social science
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Complex biological networks, comprising metabolic reactions, gene interactions, and protein interactions, often exhibit scale-free characteristics with power-law degree distributions. However, empirical studies have revealed discrepancies between observed biological network data and ideal power-law fits, highlighting the need for improved modeling approaches. To address this challenge, we propose a novel family of distributions, building upon the baseline Burr distribution. Specifically, we introduce the compounded Burr (CBurr) distribution, derived from a continuous probability distribution family, enabling flexible and efficient modeling of node degree distributions in biological networks. This study comprehensively investigates the general properties of the CBurr distribution, focusing on parameter estimation using the maximum likelihood method. Subsequently, we apply the CBurr distribution model to large-scale biological network data, aiming to evaluate its efficacy in fitting the entire range of node degree distributions, surpassing conventional power-law distributions and other benchmarks. Through extensive data analysis and graphical illustrations, we demonstrate that the CBurr distribution exhibits superior modeling capabilities compared to traditional power-law distributions. This novel distribution model holds great promise for accurately capturing the complex nature of biological networks and advancing our understanding of their underlying mechanisms.

Problem

• Modeling scale-free biological networks with deviations from power-law
• Introducing CBurr distribution for accurate network structure representation
• Validating CBurr's superiority over traditional heavy-tailed models

Innovation

• Introduces Compounded Burr (CBurr) distribution model
• Uses maximum likelihood for parameter estimation
• Validates CBurr with large-scale biological datasets