Inference for Multiple Heterogeneous Networks with a Common Invariant Subspace.

Area of Science:

• Statistical network theory
• Machine learning
• Data science

Background:

• Analyzing multiple heterogeneous networks presents challenges in modeling differences while maintaining model simplicity.
• Existing methods for single-graph analysis are insufficient for complex, multi-network inference.

Purpose of the Study:

• Introduce a novel model for analyzing multiple heterogeneous networks.
• Address the gap in methodology for multi-graph inference.
• Develop a tractable yet flexible model for network differences.

Main Methods:

• Proposed the common subspace independent-edge multiple random graph model.
• Utilized joint spectral embedding of adjacency matrices (multiple adjacency spectral embedding).
• Applied the model and embedding to simulated and real-world network data.

Main Results:

• Achieved simultaneous consistent estimation of parameters for each graph.
• Demonstrated asymptotic normality of estimates under mild assumptions.
• Showcased improvements in graph eigenvalue estimation.

Conclusions:

• The developed model and embedding method facilitate accurate inference across multiple networks.
• The approach supports various downstream tasks like dimensionality reduction, classification, and community detection.
• Successfully applied to diffusion MRI connectomes for subject classification and heterogeneity analysis.