Towards Identifiability of Interventional Stochastic Differential Equations

2025-05-21

AI Summary

This work addresses the structural identifiability of parameters in stochastic differential equation (SDE) models under multiple interventions—i.e., whether SDE parameters can be uniquely recovered from samples of post-intervention stationary distributions. Theoretically, we establish the first uniqueness guarantee for SDE parameter recovery under multi-intervention settings; for linear SDEs, we derive a tight lower bound on the minimum number of required interventions; for weak-noise nonlinear SDEs, we obtain an upper bound on identifiability. Methodologically, we propose a parametric framework featuring learnable activation functions, integrating intervention modeling, stationary distribution analysis, and weak-noise asymptotic theory. Experiments on synthetic data demonstrate that our approach accurately recovers ground-truth parameters, and the theory-guided learnable architecture significantly improves both estimation accuracy and robustness.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: State Estimation
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

We study identifiability of stochastic differential equation (SDE) models 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.

Problem

• Identifiability of SDE models under interventions
• Provable bounds for unique SDE parameter recovery
• Necessary interventions for linear and nonlinear SDEs

Innovation

• Proves bounds for unique SDE parameter recovery
• Tight bounds for linear SDE interventions
• Learnable activation functions enhance parameterization