Learning latent causal graphs via mixture oracles
This work addresses the challenge of causal inference in the presence of latent variables, which is crucial for understanding high-level features in domains like image analysis, but it appears incremental as it builds on existing mixture model techniques.
The paper tackles the problem of reconstructing causal graphical models from data with latent variables, focusing on recovering causal structure among latent variables under nonlinear dependencies, and provides conditions for identifiability and algorithms for reconstruction.
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.