Learning Early Treatment Strategy from Snapshots for mRNA-protein Regulatory Networks

Early disease detection with snapshot data has been effectively addressed by the Dynamical Network Biomarkers (DNBs) theory. After early disease detection, it is crucial to consider early medical treatment to prevent it. This paper presents a novel framework for identifying mRNA-protein regulatory systems from snapshot data and designing interventions. We estimate the state covariance of mRNA-protein expression using multi-episode snapshot samples and identify the underlying continuous-time dynamics by solving a Lyapunov-based regression problem. We provide finite-sample guarantees on the estimation accuracy of the system matrix and its dominant eigenvectors, which are essential for downstream treatment design. Building on these estimates, we formulate an optimal re-stabilization strategy that minimizes input energy with desired spectral shifts. To ensure practical feasibility, we further propose a diagonal re-stabilization scheme that identifies key regulatory nodes using a first-order eigenvalue sensitivity analysis. Validations on synthetic mRNA-protein network and real dataset demonstrate that our method accurately identifies regulatory nodes under snapshot data conditions and significantly outperforms existing baselines.