发表机构
Leiden University（莱顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究证明对线性随机动力系统每个强连通分量进行一次干预即可实现参数可辨识，并提出递归学习算法与正则化最小二乘估计器，实验验证了其有效性。
AI 中文摘要
我们研究了从稳态观测和干预数据中恢复多元Ornstein-Uhlenbeck (OU)过程参数的问题。在许多应用中，例如大规模基因扰动实验，只有静态的“快照”测量可用，这使得依赖于时间序列轨迹的标准随机微分方程估计方法不适用。我们首先建立了一个可辨识性结果：漂移图的每个强连通分量(SCC)进行一次干预，就足以在一般情况下恢复所有OU过程参数，直至一个全局缩放因子。这一结论在SCC凝聚图连通且具有单一根节点，并满足某些谱非退化假设的条件下成立。我们提出了一种递归学习算法，该算法对SCC进行拓扑排序，并为每个分量隔离其边际动态，利用为上游分量恢复的参数，从稳态矩方程中求解一个线性系统。基于这一理论基础，我们提出了一种正则化最小二乘估计器，该估计器在观测和干预数据上联合最小化稳态均值和协方差方程的残差。实验结果验证了我们在恢复底层OU过程参数方面的理论发现。
英文摘要
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.
