Causal representation learning exposes latent high-level causal variables behind low-level observations, which has enormous potential for a set of downstream tasks of interest. Despite this, identifying the true latent causal representation from observed data is a great challenge. In this work we focus on identifying latent causal variables. To this end, we analysis three intrinsic properties in latent space, including transitivity, permutation and scaling. We show that the transitivity severely hinders the identifiability of latent causal variables, while permutation and scaling guide the direction of identifying latent causal variable. To break the transitivity, we assume the underlying latent causal relations to be linear Gaussian models, in which the weights, mean and variance of Gaussian noise are modulated by an additionally observed variable. Under these assumptions we theoretically show that the latent causal variables can be identifiable up to trivial permutation and scaling. Built on this theoretical result, we propose a novel method, termed Structural caUsAl Variational autoEncoder, which directly learns latent causal variables, together with the mapping from the latent causal variables to the observed ones. Experimental results on synthetic and real data demonstrate the identifiable result and the ability of the proposed method for learning latent causal variables.
翻译:原因代表学习暴露了低层次观测背后潜在的高层次因果变量,这在一系列下游感兴趣的任务中具有巨大的潜力。尽管如此,我们仍认为从观测到的数据中找出真正的潜在因果代表是一个巨大的挑战。在这项工作中,我们侧重于查明潜在的因果变量。为此,我们分析了潜伏空间的三个内在属性,包括中转性、变异和缩放。我们表明,中转性严重阻碍潜在因果变量的可识别性,而调换和缩放则指导着潜在因果变量的识别方向。为了打破中转性,我们假设潜在的潜在因果关系是线性高斯模型,在这个模型中,高斯噪音的重量、平均值和差异由额外观察到的变量调节。根据这些假设,我们理论上表明,潜在因果变量可以被识别为微小的变异和缩放。根据这一理论结果,我们提出了一种新型方法,即结构性cus Al Variational autocorder,直接学习潜在因果变量,以及从潜在因果变量到所观测到所观测到的变量的映测结果。