Identification of Linear Non-Gaussian Latent Hierarchical Structure

Feng Xie, Biwei Huang, Zhengming Chen, Yangbo He, Zhi Geng, Kun Zhang
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:24370-24387, 2022.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-xie22a, title = {Identification of Linear Non-{G}aussian Latent Hierarchical Structure}, author = {Xie, Feng and Huang, Biwei and Chen, Zhengming and He, Yangbo and Geng, Zhi and Zhang, Kun}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {24370--24387}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/xie22a/xie22a.pdf}, url = {https://proceedings.mlr.press/v162/xie22a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Identification of Linear Non-Gaussian Latent Hierarchical Structure %A Feng Xie %A Biwei Huang %A Zhengming Chen %A Yangbo He %A Zhi Geng %A Kun Zhang %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-xie22a %I PMLR %P 24370--24387 %U https://proceedings.mlr.press/v162/xie22a.html %V 162 %X 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.
APA
Xie, F., Huang, B., Chen, Z., He, Y., Geng, Z. & Zhang, K.. (2022). Identification of Linear Non-Gaussian Latent Hierarchical Structure. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:24370-24387 Available from https://proceedings.mlr.press/v162/xie22a.html.

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