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We focus on causal discovery in the presence of measurement error in linearsystems where the mixing matrix, i.e., the matrix indicating the independentexogenous noise terms pertaining to the observed variables, is identified up topermutation and scaling of the columns. We demonstrate a somewhat surprisingconnection between this problem and causal discovery in the presence ofunobserved parentless causes, in the sense that there is a mapping, given bythe mixing matrix, between the underlying models to be inferred in theseproblems. Consequently, any identifiability result based on the mixing matrixfor one model translates to an identifiability result for the other model. Wecharacterize to what extent the causal models can be identified under atwo-part faithfulness assumption. Under only the first part of the assumption(corresponding to the conventional definition of faithfulness), the structurecan be learned up to the causal ordering among an ordered grouping of thevariables but not all the edges across the groups can be identified. We furthershow that if both parts of the faithfulness assumption are imposed, thestructure can be learned up to a more refined ordered grouping. As a result ofthis refinement, for the latent variable model with unobserved parentlesscauses, the structure can be identified. Based on our theoretical results, wepropose causal structure learning methods for both models, and evaluate theirperformance on synthetic data.

Causal Discovery in Linear Latent Variable Models Subject to Measurement Error