通过扩散偏移实现连续时间潜 SDE 的可识别性

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Abstract:Causal representation learning for time series has developed strong identifiability results in discrete-time latent causal models, but identifiability in continuous-time latent stochastic differential equation (SDE) models remains largely open. We address this gap using environment-induced shifts in diffusion covariance. We study additive-noise latent SDEs observed through an unknown nonlinear diffeomorphism, with shared drift but environment-specific diffusion covariance. We show that two diagonal diffusion regimes with pairwise distinct coordinate-wise variance ratios identify the latent coordinates up to permutation, coordinate-wise scaling, and a possible constant shift, without any sparsity assumption on the drift. We first prove this result for linear Ornstein-Uhlenbeck systems and then extend it to general additive-noise latent SDEs. Under mild smoothness, the instantaneous drift-Jacobian causal graph is identifiable up to the same permutation. We propose a two-stage estimator for latent disentanglement and optional graph recovery; experiments on synthetic systems confirm the predicted identifiability boundary, and an application to Hardanger Bridge monitoring data illustrates the approach on real sensor trajectories.

Comments:	Accepted at NeurIPS 2026 (camera-ready version). 53 pages, 15 figures
Subjects:	Machine Learning (cs.LG); Machine Learning (stat.ML)
Cite as:	arXiv:2606.28228 [cs.LG]
	(or arXiv:2606.28228v2 [cs.LG] for this version)
	https://doi.org/10.48550/arXiv.2606.28228 arXiv-issued DOI via DataCite

Submission history

From: Yuanyuan Wang [view email]
[v1] Fri, 26 Jun 2026 16:18:28 UTC (3,771 KB)
[v2] Thu, 1 Oct 2026 12:25:53 UTC (3,783 KB)