含隐混杂因子的线性 ODE 系统可辨识性分析

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Abstract:The identifiability analysis of linear Ordinary Differential Equation (ODE) systems is a necessary prerequisite for making reliable causal inferences about these systems. While identifiability has been well studied in scenarios where the system is fully observable, the conditions for identifiability remain unexplored when latent variables interact with the system. This paper aims to address this gap by presenting a systematic analysis of identifiability in linear ODE systems incorporating hidden confounders. Specifically, we investigate two cases of such systems. In the first case, latent confounders exhibit no causal relationships, yet their evolution adheres to specific functional forms, such as polynomial functions of time $t$. Subsequently, we extend this analysis to encompass scenarios where hidden confounders exhibit causal dependencies, with the causal structure of latent variables described by a Directed Acyclic Graph (DAG). The second case represents a more intricate variation of the first case, prompting a more comprehensive identifiability analysis. Accordingly, we conduct detailed identifiability analyses of the second system under various observation conditions, including both continuous and discrete observations from single or multiple trajectories. To validate our theoretical results, we perform a series of simulations, which support and substantiate our findings.

Comments:	38th Conference on Neural Information Processing Systems (NeurIPS 2024). v3: revised discrete-observation results; see Appendix D.6
Subjects:	Machine Learning (stat.ML); Machine Learning (cs.LG)
Cite as:	arXiv:2410.21917 [stat.ML]
	(or arXiv:2410.21917v3 [stat.ML] for this version)
	https://doi.org/10.48550/arXiv.2410.21917 arXiv-issued DOI via DataCite

Submission history

From: Yuanyuan Wang [view email]
[v1] Tue, 29 Oct 2024 10:15:56 UTC (392 KB)
[v2] Wed, 30 Oct 2024 05:46:38 UTC (392 KB)
[v3] Tue, 6 Oct 2026 01:16:14 UTC (389 KB)