Structural Identification of Partially Observed Linear Non-Gaussian Acyclic Model: Generalized Independent Noise Approach
Jin, Songyao
Jin, Songyao
Author
Supervisor
Department
Machine Learning
Embargo End Date
2024-01-01
Type
Thesis
Date
2024
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Language
English
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Abstract
Conventional causal discovery approaches, which seek to uncover causal relationships among measured variables, are typically sensitive to the presence of latent variables. While various methods have been developed to address this confounding issue, they often rely on strong assumptions about the underlying causal structure. In this paper, we consider a general scenario where measured and latent variables collectively form a partially observed causally sufficient linear system and latent variables may be anywhere in the causal structure. Naturally, LiNGAM, a model without latent variables, is encompassed as a special case. We theoretically show that with the aid of high-order statistics, the causal graph is (almost) fully identifiable if, roughly speaking, each latent set has a sufficient number of pure children, which can be either latent or measured. To achieve this, we leverage the Generalized Independent Noise (GIN) condition to test for statistical independence involving only measured variables in specific manners. Specifically, we first illustrate the origins of the GIN condition in terms of the data-generating process and establish the necessary and sufficient graphical criteria in its most general context. Based on the graphical criteria, we further establish the identification theorems and accordingly develop a principled algorithm for identifying the entire causal graph. The algorithm is iterative and phased, which can be flexibly altered to suit specific identifiability conditions. Afterwards, we discuss the results when the identifiability conditions are violated. Finally, experimental results show that our method effectively recovers the causal structure, even when latent variables are influenced by measured variables.
Citation
S. Jin, "Structural Identification of Partially Observed Linear Non-Gaussian Acyclic Model: Generalized Independent Noise Approach" , MS. Thesis, Machine Learning, MBZUAI, Abu Dhabi, UAE, 2024