Steady state data enables recoverable genetic network dynamics
One Intervention per Component is Enough: Towards Identifiability in Linear Stochastic Dynamics from Steady State
Machine Learning
Summary
Some experiments only capture snapshots of complex biological systems instead of continuous observations, making it hard to understand how parts influence each other over time. The authors show that by intervening on one part in each strongly connected group, it's possible to identify all parameters of the system up to a scaling factor. They provide an algorithm to recover these parameters from snapshot data and validate it with experiments. This helps scientists recover dynamic models even when detailed time recordings are unavailable.
What this means in practice
- •For genomics data analysts: Recover parameters of gene regulatory networks from steady-state gene perturbation data without needing time series measurements.
- •For systems biology modelers: Infer dynamics of biological systems split into interacting modules using minimal interventions on each module to identify model parameters.
Authors
Saber Salehkaleybar
Abstract
We study the problem of recovering the parameters of a multivariate Ornstein-Uhlenbeck (OU) process from steady-state observational and interventional data. In many applications, such as large-scale gene perturbation experiments, only stationary "snapshot" measurements are available, making standard stochastic differential equation estimation methods that rely on time-series trajectories inapplicable. We first establish an identifiability result: one intervention per strongly connected component (SCC) of the drift graph suffices to recover all OU process parameters generically up to a global scaling factor. This holds provided that the SCC condensation graph is connected with a single root and certain spectral nondegeneracy assumptions hold. We propose a recursive learning algorithm that orders SCCs topologically and, for each component, isolates its marginal dynamics and solves a linear system derived from the steady-state moment equations, leveraging parameters recovered for upstream components. Building on this theoretical foundation, we propose a regularized least-squares estimator that jointly minimizes residuals of the steady-state mean and covariance equations across observational and interventional data. Experimental results validate our theoretical findings in recovering parameters of the underlying OU process.