Towards Identifiability of Interventional Stochastic Differential Equations

We study identifiability of stochastic differential equation (SDE) models 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.

Interpretable Neural ODEs for Gene Regulatory Network Discovery under Perturbations

Modern high-throughput biological datasets with thousands of perturbations provide the opportunity for large-scale discovery of causal graphs that represent the regulatory interactions between genes. Numerous methods have been proposed to infer a directed acyclic graph (DAG) corresponding to the underlying gene regulatory network (GRN) that captures causal gene relationships. However, existing models have restrictive assumptions (e.g. linearity, acyclicity), limited scalability, and/or fail to address the dynamic nature of biological processes such as cellular differentiation. We propose PerturbODE, a novel framework that incorporates biologically informative neural ordinary differential equations (neural ODEs) to model cell state trajectories under perturbations and derive the causal GRN from the neural ODE's parameters. We demonstrate PerturbODE's efficacy in trajectory prediction and GRN inference across simulated and real over-expression datasets.