{"type":"ScholarlyArticle","title":"Some General Identification Results for Linear Latent Hierarchical Causal Structure","authors":[{"name":"Zhengming Chen","slug":"zhengming-chen","given":"Zhengming","family":"Chen","affiliation":"School of Computer Science , Guangdong University of Technology , Guangzhou , China"},{"name":"Feng Xie","slug":"feng-xie","given":"Feng","family":"Xie","affiliation":"Department of Applied Statistics , Beijing Technology and Business University , Beijing , China"},{"name":"Jie Qiao","slug":"jie-qiao","given":"Jie","family":"Qiao","affiliation":"School of Computer Science , Guangdong University of Technology , Guangzhou , China"},{"name":"Zhifeng Hao","slug":"zhifeng-hao","given":"Zhifeng","family":"Hao","affiliation":"School of Computer Science , Guangdong University of Technology , Guangzhou , China; College of Science , Shantou University , Shantou , Guangdong , China"},{"name":"Ruichu Cai","slug":"ruichu-cai","given":"Ruichu","family":"Cai","affiliation":"School of Computer Science , Guangdong University of Technology , Guangzhou , China; Peng Cheng Laboratory , Shenzhen 518066 , China"}],"abstract":"We study the problem of learning hierarchical causal structure among latent variables from measured variables. While some existing methods are able to recover the latent hierarchical causal structure, they mostly suffer from restricted assumptions, including the tree-structured graph constraint, no ``triangle\" structure, and non-Gaussian assumptions.  In this paper, we relax these restrictions above and consider a more general and challenging scenario where the beyond tree-structured graph, the ``triangle\" structure, and the arbitrary noise distribution are allowed. We investigate the identifiability of the latent hierarchical causal structure and show that by using second-order statistics, the latent hierarchical structure can be identified up to the Markov equivalence classes over latent variables. Moreover, some directions in the Markov equivalence classes of latent variables can be further identified using partially non-Gaussian data. Based on the theoretical results above, we design an effective algorithm for learning the latent hierarchical causal structure. The experimental results on synthetic data verify the effectiveness of the proposed method.","doi":"10.24963/ijcai.2023/397","url":"https://ijcai.org/proceedings/2023/397","pdf":"https://ijcai.org/proceedings/2023/0397.pdf","markdown":"https://ijcai.org/proceedings/2023/397.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/397","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Machine Learning","track":"Main Track","number":397,"pages":{"first":3568,"last":3576},"keywords":["Uncertainty in AI: UAI: Causality, structural causal models and causal inference","Machine Learning: ML: Causality"],"videos":[],"references":[{"position":1,"raw":"[Adams et al., 2021] J. 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