@inproceedings{21113,
  abstract     = {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 induced by a structural causal model, and additional data from (in the best case) 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.},
  author       = {Montagna, Francesco},
  booktitle    = {The 14th International Conference on Learning Representations},
  location     = {Rio de Janeiro, Brazil},
  publisher    = {OpenReview},
  title        = {{On the identifiability of causal graphs with multiple environments}},
  year         = {2026},
}

@article{20934,
  abstract     = { Supervised learning for causal discovery from observational data often achieves competitive performance despite seemingly avoiding the explicit assumptions that traditional methods require for identifiability. In this work, we analyze CSIvA (Ke et al., 2023) on bivariate causal models, a transformer architecture for amortized inference promising to train on synthetic data and transfer to real ones. First, we bridge the gap with identifiability theory, showing that the training distribution implicitly defines a prior on the causal model of the test observations: consistent with classical approaches, good performance is achieved when we have a good prior on the test data, and the underlying model is identifiable. Second, we find that CSIvA can not generalize to classes of causal models unseen during training: to overcome this limitation, we theoretically and empirically analyze \textit{when} training CSIvA on datasets generated by multiple identifiable causal models with different structural assumptions improves its generalization at test time. Overall, we find that amortized causal discovery still adheres to identifiability theory, violating the previous hypothesis from Lopez-Paz et al. (2015) that supervised learning methods could overcome its restrictions.},
  author       = {Montagna, Francesco and Cairney-Leeming, Maximilian T and Sridhar, Dhanya and Locatello, Francesco},
  issn         = {2835-8856},
  journal      = {Transactions on Machine Learning Research},
  publisher    = {ML Research Press},
  title        = {{Demystifying amortized causal discovery with transformers}},
  year         = {2025},
}