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 measurement models without 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. 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条件下可识别且可从潜在空间中的未知干预进行重构的条件。主要关注点在于无需线性或高斯性等参数假设的测量模型中潜在结构的识别。此外，我们不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。这拓展了近期关于从观测与干预中学习因果表征的研究。证明过程具有构造性，并引入了两个新的图论概念——虚子集与孤立边——这些概念本身可能具有独立价值。作为独立兴趣点，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。这是首批在无参数假设、未知干预及无忠实性条件下，刻画因果表征可识别性条件的成果。