🤖 AI Summary
This study addresses the challenge of spurious edge generation when reconstructing causal regulatory networks of dynamical systems from discrete-state trajectories. The authors propose a modeling framework based on integral-form additive nonparametric ordinary differential equations, which accommodates both dense and sparse irregular sampling. By incorporating a data-driven edge selection mechanism, the method effectively suppresses false connections while inferring time-varying, weighted, bidirectional causal relationships between nodes, including activation or inhibition effects. This enables the construction of interpretable, symbolic causal networks. In five simulation experiments, the approach substantially outperforms GRADE, reducing spurious edges from 239 to zero in the most challenging scenario while nearly preserving all true regulatory links, thereby achieving high-precision dynamic network reconstruction.
📝 Abstract
Learning a dynamical system and reconstructing the underlying regulatory network from $p$ discretely observed state trajectories remain challenging problems. Existing approaches often produced a large number of spurious edges and suffered from several methodological limitations. We propose a new approach, Reconstruction of Enhanced Causal Omnidirectional Network (RECON), that leverages an integral-based additive nonparametric ODE model to reconstruct regulatory networks from $p$ time-course data. RECON incorporates five methodological advances. First, it incorporates a new data-driven edge selection procedure that substantially reduces spurious edges while preserving true regulatory edges. Second, it reconstructs an omnidirectional network that captures causal regulatory relationships rather than merely statistical associations or noise artifacts. Third, it substantially broadens the applicability of standard ODE-based approaches by accommodating both dense regular and sparse irregular longitudinal sampling scenarios. Fourth, it models both node trajectories and edge regulatory effects as time-varying functions, emphasizing a dynamic regulatory network. Fifth, it reconstructs a signed and weighted regulatory network and provides comprehensive network interpretation through two-way direction, activatory/inhibitory indicator, and strength, together with keystone node identification and topological structure. Across five simulation studies, RECON consistently outperforms GRADE by removing nearly all spurious edges while retaining nearly all true regulatory edges, resulting in highly accurate network reconstruction. In the most challenging scenario, the number of spurious edges is reduced from 239 to 0.