BY RINA FOYGEL BARBER1,a, MATHIAS DRTON2,b, NILS STURMA2,c AND LUCA WEIHS3,d

• 成果类型: Article
• 署名作者: Barber, Rina Foygel; Drton, Mathias; Sturma, Nils; Weihs, Luca
• 署名单位: University of Chicago; Technical University of Munich
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/22-AOS2221
• 发表日期: 2022
• 页码: 3174-3196
• 关键词: generic identifiability; models

摘要

We consider linear structural equation models with latent variables and develop a criterion to certify whether the direct causal effects between the ob-servable variables are identifiable based on the observed covariance matrix. Linear structural equation models assume that both observed and latent vari-ables solve a linear equation system featuring stochastic noise terms. Each model corresponds to a directed graph whose edges represent the direct ef-fects that appear as coefficients in the equation system. Prior research has developed a variety of methods to decide identifiability of direct effects in a latent projection framework, in which the confounding effects of the latent variables are represented by correlation among noise terms. This approach is effective when the confounding is sparse and effects only small subsets of the observed variables. In contrast, the new latent-factor half-trek crite-rion (LF-HTC) we develop in this paper operates on the original unprojected latent variable model and is able to certify identifiability in settings, where some latent variables may also have dense effects on many or even all of the observables. Our LF-HTC is an effective sufficient criterion for rational identifiability, under which the direct effects can be uniquely recovered as rational functions of the joint covariance matrix of the observed random vari-ables. When restricting the search steps in LF-HTC to consider subsets of latent variables of bounded size, the criterion can be verified in time that is polynomial in the size of the graph.