Identification of Partially Observed Linear Causal Models: Graphical Conditions for the Non-Gaussian and Heterogeneous Cases
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Identification of Partially Observed Linear Causal Models: Graphical Conditions for the Non-Gaussian and Heterogeneous Cases. / Adams, Jeffrey Glenn; Hansen, Niels Richard; Zhang, Kun.
Advances in Neural Information Processing Systems 34 (NeurIPS). NeurIPS Proceedings, 2021. p. 1-12.Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
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TY - GEN
T1 - Identification of Partially Observed Linear Causal Models: Graphical Conditions for the Non-Gaussian and Heterogeneous Cases
AU - Adams, Jeffrey Glenn
AU - Hansen, Niels Richard
AU - Zhang, Kun
PY - 2021
Y1 - 2021
N2 - In causal discovery, linear non-Gaussian acyclic models (LiNGAMs) have been studied extensively. While the causally sufficient case is well understood, in many real problems the observed variables are not causally related. Rather, they are generated by latent variables, such as confounders and mediators, which may themselves be causally related. Existing results on the identification of the causal structure among the latent variables often require very strong graphical assumptions. In this paper, we consider partially observed linear models with either non-Gaussian or heterogeneous errors. In that case we give two graphical conditions which are necessary for identification of the causal structure. These conditions are closely related to sparsity of the causal edges. Together with one additional condition on the coefficients, which holds generically for any graph, the two graphical conditions are also sufficient for identifiability. These new conditions can be satisfied even when there is a large number of latent variables. We demonstrate the validity of our results on synthetic data.
AB - In causal discovery, linear non-Gaussian acyclic models (LiNGAMs) have been studied extensively. While the causally sufficient case is well understood, in many real problems the observed variables are not causally related. Rather, they are generated by latent variables, such as confounders and mediators, which may themselves be causally related. Existing results on the identification of the causal structure among the latent variables often require very strong graphical assumptions. In this paper, we consider partially observed linear models with either non-Gaussian or heterogeneous errors. In that case we give two graphical conditions which are necessary for identification of the causal structure. These conditions are closely related to sparsity of the causal edges. Together with one additional condition on the coefficients, which holds generically for any graph, the two graphical conditions are also sufficient for identifiability. These new conditions can be satisfied even when there is a large number of latent variables. We demonstrate the validity of our results on synthetic data.
M3 - Article in proceedings
SP - 1
EP - 12
BT - Advances in Neural Information Processing Systems 34 (NeurIPS)
PB - NeurIPS Proceedings
T2 - 35th Conference on Neural Information Processing Systems (NeurIPS 2021)
Y2 - 6 December 2021 through 14 December 2021
ER -
ID: 304277539