In recent years the possibility of relaxing the so- called Faithfulness assumption in automated causal discovery has been investigated. The investiga- tion showed (1) that the Faithfulness assumption can be weakened in various ways that in an impor- tant sense preserve its power, and (2) that weak- ening of Faithfulness may help to speed up meth- ods based on Answer Set Programming. However, this line of work has so far only considered the dis- covery of causal models without latent variables. In this paper, we study weakenings of Faithfulness for constraint-based discovery of semi-Markovian causal models, which accommodate the possibility of latent variables, and show that both (1) and (2) remain the case in this more realistic setting.
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Causal Discovery in Linear Latent Variable Models Subject to Measurement Error
We focus on causal discovery in the presence of measurement error in linear systems where the mixing matrix, i.e., the matrix indicating the independent exogenous noise terms pertaining to the observed variables, is identified up to permutation and scaling of the columns. We demonstrate a somewhat surprising connection between this problem and causal discovery in the presence of unobserved parentless causes, in the sense that there is a mapping, given by the mixing matrix, between the underlying models to be inferred in these problems. Consequently, any identifiability result based on the mixing matrix for one model translates to an identifiability result for the other model. We characterize to what extent the causal models can be identified under a two-part faithfulness assumption. Under only the first part of the assumption (corresponding to the conventional definition of faithfulness), the structure can be learned up to the causal ordering among an ordered grouping of the variables but not all the edges across the groups can be identified. We further show that if both parts of the faithfulness assumption are imposed, the structure can be learned up to a more refined ordered grouping. As a result of this refinement, for the latent variable model with unobserved parentless causes, the structure can be identified. Based on our theoretical results, we propose causal structure learning methods for both models, and evaluate their performance on synthetic data.
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- Award ID(s):
- 1942239
- NSF-PAR ID:
- 10410533
- Editor(s):
- S. Koyejo; S. Mohamed; A. Agarwal; D. Belgrave; K. Cho, A. Oh
- Date Published:
- Journal Name:
- Advances in Neural Information Processing Systems 35 (NeurIPS 2022)
- Volume:
- 35
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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