The task of causal representation learning aims to uncover latent higher-level causal representations that affect lower-level observations. Identifying true latent causal representations from observed data, while allowing instantaneous causal relations among latent variables, remains a challenge, however. To this end, we start from the analysis of three intrinsic properties in identifying latent space from observations: transitivity, permutation indeterminacy, and scaling indeterminacy. We find that transitivity acts as a key role in impeding the identifiability of latent causal representations. To address the unidentifiable issue due to transitivity, we introduce a novel identifiability condition where the underlying latent causal model satisfies a linear-Gaussian model, in which the causal coefficients and the distribution of Gaussian noise are modulated by an additional observed variable. Under some mild assumptions, we can show that the latent causal representations can be identified up to trivial permutation and scaling. Furthermore, based on this theoretical result, we propose a novel method, termed Structural caUsAl Variational autoEncoder, which directly learns latent causal representations and causal relationships among them, together with the mapping from the latent causal variables to the observed ones. We show that the proposed method learns the true parameters asymptotically. Experimental results on synthetic and real data demonstrate the identifiability and consistency results and the efficacy of the proposed method in learning latent causal representations.
翻译:然而,为了达到这一目的,我们从分析三个内在特性开始,从观察中找出潜在的空间:过渡性、变异性、不确定性以及扩大不确定性。我们发现,过渡性是阻碍潜在因果关系陈述可辨别性的一个关键作用。为了解决因过渡性造成的无法辨别的问题,我们引入了一种新的可辨识性条件,即潜在因果关系模型符合线性-加苏西模式,其中因果系数和高斯噪音的分布由观察到的可辨别变量加以调节。根据一些温和的假设,我们可以表明,潜在因果关系表述可被确定为微不足道的变异和升级。此外,根据这一理论结果,我们提出了一种新型方法,称为结构性CASAl Variational 自动Encoder,直接学习潜在因果关系和因果关系,其中潜在的因果关系模式由线性-加苏西模型调节,其中因果系数和高斯噪音的分布由观察到的可辨识异性变量调节。我们从所观测到的正因果性模型中学习真实性,从所观测到的正因果性模型,从所观察到的正因果性变量到真实性分析结果。