DeepBLNet: Bilevel Network Learning via Hierarchically Structured Sparsity
Jiayi Fan, Jingyuan Yang, Shuangge Ma, Mengyun Wu
Accurate network estimation serves as the cornerstone for understanding complex systems across scientific domains, spanning from decoding gene regulatory pathways in systems biology to identifying social interaction patterns in computational sociology. Modern applications demand methods that simultaneously address two critical challenges: capturing nonlinear interdependencies between variables and recovering inherent hierarchical structures where higher-level entities coordinate lower-level components (e.g., functional pathways organizing gene clusters). Traditional Gaussian graphical models fundamentally fail in these aspects due to their restrictive linear assumptions and flat network representations. We propose DeepBLNet, a deep learning framework for bi-level network inference. The core innovation lies in hierarchical selection layers that enforce structural consistency between high-level interaction groups and their constituent low-level connections via adaptive sparsity constraints. This architecture is integrated with compositional deep architectures that learn cross-level interaction patterns through constrained nonlinear transformations, explicitly preserving hierarchical dependencies while overcoming the representational limitations of linear methods. Crucially, we establish formal theoretical guarantees for consistent recovery of both high-level interactions and their internal low-level structures under general statistical regimes. Extensive validation demonstrates DeepBLNet's effectiveness across synthetic and real-world scenarios, achieving superior F1 scores compared to competitive methods and particularly benefiting complex systems analysis through its interpretable bilevel structure discovery.