Nonparametric Inference of Higher Order Interaction Patterns in Networks

Conceitos Básicos

Proposing a method for inferring higher order interactions in networks using non-parametric priors and generative models.

Resumo

Introduces a method for decomposing networks into higher order interactions.
Analyzes the importance of higher order structures in network organization.
Discusses challenges in quantifying higher order network structures.
Presents a nonparametric Bayesian approach for inferring higher order interactions.
Compares different models for network representation and selection.
Provides insights from empirical results on various networks.

Estatísticas

"For instance, many real–world networks contain certain small connectivity patterns, known as network motifs, in much larger numbers than expected in random graphs with conditionally independent edges [1]."
"In undirected networks there are 11117 different ways of connecting 8 vertices and in directed networks there are 9364 such motifs on just 5 vertices."

Citações

"The reduction of large complex systems to elementary units and their interactions is one of the primary modes of operation in science."
"Our results demonstrate that many empirical networks can be represented more parsimoniously by including higher order interaction in their representations."

Principais Insights Extraídos De

Nonparametric inference of higher order interaction patterns in networks

by Anatol E. We... às arxiv.org 03-26-2024

https://arxiv.org/pdf/2403.15635.pdf

Perguntas Mais Profundas

How can incorporating more general intersections between higher order subgraphs enhance the inference process

Incorporating more general intersections between higher order subgraphs can enhance the inference process by allowing for a more nuanced representation of complex network structures. By considering overlaps or shared vertices between different motifs, the model can capture more intricate relationships and dependencies within the network. This approach enables the identification of composite patterns that involve multiple subgraphs interacting in specific ways, leading to a richer understanding of the network's organization and functionality. Additionally, incorporating general intersections can help uncover hidden connections and structural regularities that may not be apparent when only considering non-overlapping subgraphs.

What are the limitations or potential biases introduced by using degree-corrected models

Using degree-corrected models introduces limitations and potential biases in the inference process. One limitation is that these models assume a certain level of homogeneity or regularity in the distribution of atomic degrees across vertices, which may not always reflect real-world networks' inherent heterogeneity. This assumption could lead to oversimplified representations or inaccurate estimations of higher order interactions in networks with diverse node degrees. Additionally, degree-corrected models might introduce biases towards certain types of motifs or structures based on their prevalence in the data, potentially overlooking less common but significant patterns present in the network.

How might community structures be integrated into generative models to capture multi-scale structures

Integrating community structures into generative models offers a promising approach to capturing multi-scale structures within networks. By incorporating information about communities or clusters of nodes with dense internal connections and sparser external connections, these models can better represent how different parts of a network interact at various scales. Community-aware generative models could consider how higher order interactions manifest within and between communities, providing insights into modular organization and functional relationships within complex networks. This integration allows for a more comprehensive analysis that accounts for both local interactions within communities and global connectivity patterns across them.