On the identifiability of causal graphs with multiple environments
This provides a foundational advance for researchers in causal inference by enabling full graph recovery with minimal auxiliary data, though it is incremental in relaxing constraints from prior work.
The paper tackles the problem of causal discovery from observational data, which is generally ill-posed, by showing that with access to data from only two environments that differ in noise statistics, the unique causal graph becomes identifiable, even with arbitrary nonlinear mechanisms.
Causal discovery from i.i.d. observational data is known to be generally ill-posed. We demonstrate that if we have access to the distribution of a structural causal model, and additional data from only two environments that sufficiently differ in the noise statistics, the unique causal graph is identifiable. Notably, this is the first result in the literature that guarantees the entire causal graph recovery with a constant number of environments and arbitrary nonlinear mechanisms. Our only constraint is the Gaussianity of the noise terms; however, we propose potential ways to relax this requirement. Of interest on its own, we expand on the well-known duality between independent component analysis (ICA) and causal discovery; recent advancements have shown that nonlinear ICA can be solved from multiple environments, at least as many as the number of sources: we show that the same can be achieved for causal discovery while having access to much less auxiliary information.