On the Parameter Identifiability of Partially Observed Linear Causal Models
Dong, Xinshuai Ng, Ignavier Huang, Biwei Sun, Yuewen Jin, Songyao Legaspi, Roberto Spirtes, Peter Zhang, Kun
Dong, Xinshuai
Ng, Ignavier
Huang, Biwei
Sun, Yuewen
Jin, Songyao
Legaspi, Roberto
Spirtes, Peter
Zhang, Kun
Supervisor
Department
Machine Learning
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Type
Conference proceeding
Date
2024
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Language
English
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Abstract
Linear causal models are important tools for modeling causal dependencies and yet in practice, only a subset of the variables can be observed. In this paper, we examine the parameter identifiability of these models by investigating whether the edge coefficients can be recovered given the causal structure and partially observed data. Our setting is more general than that of prior research—we allow all variables, including both observed and latent ones, to be flexibly related, and we consider the coefficients of all edges, whereas most existing works focus only on the edges between observed variables. Theoretically, we identify three types of indeterminacy for the parameters in partially observed linear causal models. We then provide graphical conditions that are sufficient for all parameters to be identifiable and show that some of them are provably necessary. Methodologically, we propose a novel likelihood-based parameter estimation method that addresses the variance indeterminacy of latent variables in a specific way and can asymptotically recover the underlying parameters up to trivial indeterminacy. Empirical studies on both synthetic and real-world datasets validate our identifiability theory and the effectiveness of the proposed method in the finite-sample regime.
Citation
X. Dong et al., “On the Parameter Identifiability of Partially Observed Linear Causal Models,” Adv Neural Inf Process Syst, vol. 37, pp. 30740–30771, Dec. 2024, Accessed: Mar. 24, 2025. [Online]. Available: https://github.com/dongxinshuai/scm-identify.
Source
Advances in Neural Information Processing Systems (NeurIPS 2024)
Conference
Keywords
Parameter identifiability, Partially observed linear causal models, Edge coefficient recovery, Graphical conditions, Likelihood-based estimation?
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Publisher
NEURIPS