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Traditional causal discovery methods mainly focus on estimating causal relations among measured variables, but in many real-world problems, such as questionnaire-based psychometric studies, measured variables are generated by latent variables that are causally related. Accordingly, this paper investigates the problem of discovering the hidden causal variables and estimating the causal structure, including both the causal relations among latent variables and those between latent and measured variables. We relax the frequently-used measurement assumption and allow the children of latent variables to be latent as well, and hence deal with a specific type of latent hierarchical causal structure. In particular, we define a minimal latent hierarchical structure and show that for linear non-Gaussian models with the minimal latent hierarchical structure, the whole structure is identifiable from only the measured variables. Moreover, we develop a principled method to identify the structure by testing for Generalized Independent Noise (GIN) conditions in specific ways. Experimental results on both synthetic and real-world data show the effectiveness of the proposed approach. 

An important problem across multiple disciplines is to infer and understand meaningful latent variables. One strategy commonly used is to model the measured variables in terms of the latent variables under suitable assumptions on the connectivity from the latents to the measured (known as measurement model). Furthermore, it might be even more interesting to discover the causal relations among the latent variables (known as structural model). Recently, some methods have been proposed to estimate the structural model by assuming that the noise terms in the measured and latent variables are non-Gaussian. However, they are not suitable when some of the noise terms become Gaussian. To bridge this gap, we investigate the problem of identification of the structural model with arbitrary noise distributions. We provide necessary and sufficient condition under which the structural model is identifiable: it is identifiable iff for each pair of adjacent latent variables Lx, Ly, (1) at least one of Lx and Ly has non-Gaussian noise, or (2) at least one of them has a non-Gaussian ancestor and is not d-separated from the non-Gaussian component of this ancestor by the common causes of Lx and Ly. This identifiability result relaxes the non-Gaussianity requirements to only a (hopefully small) subset of variables, and accordingly elegantly extends the application scope of the structural model. Based on the above identifiability result, we further propose a practical algorithm to learn the structural model. We verify the correctness of the identifiability result and the effectiveness of the proposed method through empirical studies. 

This paper investigates the problem of selecting instrumental variables relative to a target causal influence X→Y from observational data generated by linear non-Gaussian acyclic causal models in the presence of unmeasured confounders. We propose a necessary condition for detecting variables that cannot serve as instrumental variables. Unlike many existing conditions for continuous variables, i.e., that at least two or more valid instrumental variables are present in the system, our condition is designed with a single instrumental variable. We then characterize the graphical implications of our condition in linear non-Gaussian acyclic causal models. Given that the existing graphical criteria for the instrument validity are not directly testable given observational data, we further show whether and how such graphical criteria can be checked by exploiting our condition. Finally, we develop a method to select the set of candidate instrumental variables given observational data. Experimental results on both synthetic and real-world data show the effectiveness of the proposed method.