We study the problem of reconstructing a causal graphical model from data in
the presence of latent variables. The main problem of interest is recovering
the causal structure over the latent variables while allowing for general,
potentially nonlinear dependence between the variables. In many practical
problems, the dependence between raw observations (e.g. pixels in an image) is
much less relevant than the dependence between certain high-level, latent
features (e.g. concepts or objects), and this is the setting of interest. We
provide conditions under which both the latent representations and the
underlying latent causal model are identifiable by a reduction to a mixture
oracle. These results highlight an intriguing connection between the
well-studied problem of learning the order of a mixture model and the problem
of learning the bipartite structure between observables and unobservables. The
proof is constructive, and leads to several algorithms for explicitly
reconstructing the full graphical model. We discuss efficient algorithms and
provide experiments illustrating the algorithms in practice.

研究了在存在潜在变量的数据中重构因果图模型的问题，提出通过将其还原为混合预言机来确定潜在表示和潜在因果模型，从而揭示了混合模型顺序学习和可观测和不可观测之间的双分图结构学习问题之间的联系，并提供了几个重构完整图模型的算法。