We establish conditions under which latent causal graphs are nonparametrically identifiable and can be reconstructed from unknown interventions in the latent space. Our primary focus is the identification of the latent structure in a measurement model, i.e. causal graphical models where dependence between observed variables is insignificant compared to dependence between latent representations, without making parametric assumptions such as linearity or Gaussianity. Moreover, we do not assume the number of hidden variables is known, and we show that at most one unknown intervention per hidden variable is needed. This extends a recent line of work on learning causal representations from observations and interventions. The proofs are constructive and introduce two new graphical concepts -- imaginary subsets and isolated edges -- that may be useful in their own right. As a matter of independent interest, the proofs also involve a novel characterization of the limits of edge orientations within the equivalence class of DAGs induced by unknown interventions. Experiments confirm that the latent graph can be recovered from data using our theoretical results. These are the first results to characterize the conditions under which causal representations are identifiable without making any parametric assumptions in a general setting with unknown interventions and without faithfulness.

翻译：我们建立了潜在因果图在非参数意义下可辨识且能通过未知干预在潜在空间中进行重建的条件。主要关注测量模型中潜在结构的辨识问题，即观测变量间的依赖关系远弱于潜在表示间依赖关系的因果图模型，且无需线性或高斯性等参数假设。此外，我们未假设隐变量数量已知，并证明每个隐变量最多需要一个未知干预。这拓展了近期关于通过观测与干预学习因果表示的研究。证明具有构造性，并引入两个可能具有独立意义的新图论概念——虚子集与孤立边。作为独立关注点，证明还包含对未知干预诱导的有向无环图等价类中边方向限制的新颖刻画。实验证实我们的理论结果可从数据中恢复潜在图。这是首个在一般场景下无需参数假设、允许未知干预且不依赖忠实性条件即可刻画因果表示可辨识性条件的研究成果。