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About this paper
Nils Sturma, Chandler Squires, Mathias Drton, Caroline Uhler
Sturma et al. (NeurIPS 2023) establishes conditions under which latent causal structures and full joint distributions can be uniquely recovered from unpaired, multi-domain observed data in linear structural equation models. The work provides a two-step algorithmic framework for this recovery and demonstrates its efficacy in simulations.
Key insights
- Pairwise distinct, non-symmetric, and non-Gaussian latent error distributions are crucial for uniquely identifying the overall mixing matrix and reconstructing the full joint distribution from unpaired marginals.
- The 'two partial pure children' sparsity condition on observed variables provides sufficient information to uniquely identify the causal graph among shared latent variables.
- The challenge of recovering a joint distribution from unpaired marginals can be addressed by leveraging principles from Independent Component Analysis (ICA) across multiple domains.
Summary by alphaXiv.
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