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.

本文介绍了一种在潜在空间中通过未知干预重建潜在因果图的方法，不需要进行参数假设，并且不需要已知潜在变量的数量，每个潜在变量最多只需要一个未知干预，通过引入虚集和孤立边的两个新图形概念，可构造性地证明了这种方法的可行性。