One Intervention per Component is Enough: Towards Identifiability in Linear Stochastic Dynamics from Steady State

2026-09-17

AI Summary

研究通过稳态观测和干预数据恢复多变量OU过程参数的问题，提出一种仅需每个强连通分量一次干预的方法，并结合递归学习算法与正则化最小二乘估计器来解决。

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.

Problem

• multivariate Ornstein-Uhlenbeck process
• steady-state data
• interventional data
• parameter recovery
• identifiability

Innovation

• identifiability
• intervention per SCC
• steady-state data
• recursive learning algorithm
• regularized least-squares estimator