Presentation 2-2, 3:30PM~3:50PM KST.
Speaker
Junhyoung Chung (Seoul National University)
Title
Learning distribution-free anchored linear structural equation models in the presence of measurement error.
Abstract
This presentation tackles the challenge of identifiability in distribution-free anchored linear structural equation models (SEMs), where observed variables are imperfect measures for target variables, and the error distributions are not restricted to being Gaussian. We introduce the geometry-faithfulness assumption, ensuring that partial correlations serve as direct indicators of d-separation/connection. The identifiability of distribution-free anchored linear SEMs can be achieved under the same identifiability conditions for anchored Gaussian linear SEMs, but by replacing the faithfulness assumption with the geometry-faithfulness assumption. Moreover, it shows that a learning algorithm leveraging the PC algorithm with Fisher's z-test, originally designed for anchored Gaussian linear SEMs, remains applicable and effective for distribution-free anchored linear SEMs. It also provides statistical guarantees for the proposed algorithm, including the strong geometry-faithfulness assumption, ensuring its consistency. These theoretical contributions are validated through extensive numerical experiments and the analysis of real galaxy data.