首次证明干预下SDE参数可唯一恢复，为因果建模提供理论支撑。
Towards Identifiability of Interventional Stochastic Differential Equations
- 基于多干预数据，推导线性SDE所需最少干预次数
- 小噪声下给出非线性SDE参数恢复的上界
- 在基因调控建模中验证可学习激活函数的优势
我们研究了在多重干预条件下随机微分方程（SDE）的可识别性。结果首次给出了在给定其平稳分布样本时，唯一恢复SDE参数的可证明边界。针对线性SDE，我们给出了必要干预次数的紧致下界；在小噪声条件下，对非线性SDE给出了参数恢复的上界。通过合成数据实验验证了真实参数的可恢复性，并基于理论结果，在基因调控动力学应用中展示了可学习激活函数参数化的优势。
原文摘要 · Abstract (English)
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.
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