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 dependencies.
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.
more »
« less
This content will become publicly available on September 17, 2025
Learning nonparametric latent causal graphs with unknown interventions
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.
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- Award ID(s):
- 1956330
- PAR ID:
- 10542245
- Publisher / Repository:
- Advances in Neural Information Processing Systems 36 (NeurIPS 2023) Main Conference Track
- Date Published:
- Subject(s) / Keyword(s):
- graphical models directed acyclic graphs causality identifiability causal representation learning unknown interventions
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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