Towards Identifiability of Interventional Stochastic Differential Equations

Aaron Zweig, Zaikang Lin, Elham Azizi, David A. Knowles
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:8349-8374, 2026.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-zweig26a, title = {Towards Identifiability of Interventional Stochastic Differential Equations}, author = {Zweig, Aaron and Lin, Zaikang and Azizi, Elham and Knowles, David A.}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {8349--8374}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/zweig26a/zweig26a.pdf}, url = {https://proceedings.mlr.press/v337/zweig26a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Towards Identifiability of Interventional Stochastic Differential Equations %A Aaron Zweig %A Zaikang Lin %A Elham Azizi %A David A. Knowles %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-zweig26a %I PMLR %P 8349--8374 %U https://proceedings.mlr.press/v337/zweig26a.html %V 337 %X 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.
APA
Zweig, A., Lin, Z., Azizi, E. & Knowles, D.A.. (2026). Towards Identifiability of Interventional Stochastic Differential Equations. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:8349-8374 Available from https://proceedings.mlr.press/v337/zweig26a.html.

Related Material