Zaikang Lin | Searcharxiv

arXiv2025

Towards Identifiability of Interventional Stochastic Differential Equations

We study identifiability of stochastic differential equations (SDE) under multiple interventions. Our results give the first provable bounds for unique recovery of SDE parameters given samples from their stationary distributions. We give tight bounds on the number of necessary interventions for linear SDEs, and upper bounds for nonlinear SDEs in the small noise regime. We experimentally validate the recovery of true parameters in synthetic data, and motivated by our theoretical results, demonstrate the advantage of parameterizations with learnable activation functions in application to gene regulatory dynamics.

cs.LG↗

arXiv2025

Interpretable Neural ODEs for Gene Regulatory Network Discovery under Perturbations

Modern high-throughput biological datasets containing thousands of perturbations enable large-scale discovery of causal graphs that represent regulatory interactions between genes. Differentiable causal graphical models and regression-based methods have been developed to infer gene regulatory networks (GRNs) from interventional datasets. However, existing approaches fail to capture the non-linear dynamics of biological processes such as cellular differentiation. To address this limitation, we propose PerturbODE, a novel framework that employs interpretable neural ordinary differential equations (neural ODEs) to model cell state trajectories under perturbations and derive the underlying causal GRN from the neural ODE parameters, enabling downstream simulation of unseen genetic interventions. The GRN is encoded via a single-hidden-layer feedforward network, implicitly grouping genes into interpretable co-regulated modules. We demonstrate PerturbODE's efficacy in GRN inference and extension to perturbation response prediction across both simulated and real overexpression datasets.

cs.LG↗