Causal discovery of 1-factor measurement models in linear latent variable models with arbitrary noise distributions

Authors

Feng Xie, Beijing Technology & Business University
Yan Zeng, Tsinghua University
Zhengming Chen, Guangdong University of Technology
Yangbo He, Peking University
Zhi Geng, Beijing Technology & Business University
Kun Zhang, Carnegie Mellon University & Mohamed bin Zayed University of Artificial IntelligenceFollow

Document Type

Article

Publication Title

Neurocomputing

Abstract

The problem of causal discovery is especially challenging when the variables of interest cannot be directly measured. In measurement models, the measured variables were generated by latent causal variables that are causally related to each other, and by estimating the measurement model from measured data, one is able to recover the latent variables and their causal relations. In this paper, we provide precise sufficient identifiability conditions for the linear pure measurement model, and show what information of the causal structure can be recovered from observed data without prior knowledge of data distributions. In particular, we first show that, based on second-order statistics, although the pure measurement model is in general not fully identifiable under the assumption of two pure measurement variables, we can identify the set of all candidate measurement models. We then further prove that the pure measurement model can be identified uniquely based on higher-order statistics. Next, to address more general situations, we offer the identifiability conditions of linear measurement models with arbitrary noise distributions. We finally develop a unified method to learn pure measurement models from data. Experimental results on both synthetic and real-world data demonstrate the usefulness of our theory and the effectiveness of our approach.

First Page

48

Last Page

61

DOI

10.1016/j.neucom.2023.01.034

Publication Date

3-14-2023

Keywords

Causal discovery, Latent causal structure, Latent variable models, Measurement model

Comments

IR Deposit conditions:

OA version (pathway a) Accepted version

License: CC BY-NC-ND

Must link to publisher version with DOI Authors can share their accepted manuscript immediately by updating a preprint in arXiv or RePEc with the accepted manuscript

Recommended Citation

Xie, F., Zeng, Y., Chen, Z., He, Y., Geng, Z., and Zhang, K., "Causal discovery of 1-factor measurement models in linear latent variable models with arbitrary noise distributions", Neurocomputing, vol. 526, p. 48-61, March 2023, doi: 10.1016/j.neucom.2023.01.034