---
OA_place: publisher
OA_type: gold
_id: '21113'
abstract:
- lang: eng
text: '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.'
article_processing_charge: No
arxiv: 1
author:
- first_name: Francesco
full_name: Montagna, Francesco
id: 353afc8e-19f4-11f0-9db9-811f1723c83f
last_name: Montagna
citation:
ama: 'Montagna F. On the identifiability of causal graphs with multiple environments.
In: The 14th International Conference on Learning Representations. OpenReview.'
apa: 'Montagna, F. (n.d.). On the identifiability of causal graphs with multiple
environments. In The 14th International Conference on Learning Representations.
Rio de Janeiro, Brazil: OpenReview.'
chicago: Montagna, Francesco. “On the Identifiability of Causal Graphs with Multiple
Environments.” In The 14th International Conference on Learning Representations.
OpenReview, n.d.
ieee: F. Montagna, “On the identifiability of causal graphs with multiple environments,”
in The 14th International Conference on Learning Representations, Rio de
Janeiro, Brazil.
ista: 'Montagna F. On the identifiability of causal graphs with multiple environments.
The 14th International Conference on Learning Representations. ICLR: International
Conference on Learning Representations.'
mla: Montagna, Francesco. “On the Identifiability of Causal Graphs with Multiple
Environments.” The 14th International Conference on Learning Representations,
OpenReview.
short: F. Montagna, in:, The 14th International Conference on Learning Representations,
OpenReview, n.d.
conference:
end_date: 2026-04-27
location: Rio de Janeiro, Brazil
name: 'ICLR: International Conference on Learning Representations'
start_date: 2026-04-23
corr_author: '1'
date_created: 2026-01-30T08:16:25Z
date_published: 2026-02-11T00:00:00Z
date_updated: 2026-02-16T08:15:11Z
day: '11'
ddc:
- '000'
department:
- _id: FrLo
external_id:
arxiv:
- '2510.13583'
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2510.13583
month: '02'
oa: 1
oa_version: Published Version
publication: The 14th International Conference on Learning Representations
publication_status: accepted
publisher: OpenReview
status: public
title: On the identifiability of causal graphs with multiple environments
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2026'
...
---
OA_place: publisher
OA_type: gold
PlanS_conform: '1'
_id: '20934'
abstract:
- lang: eng
text: ' 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.'
alternative_title:
- TMLR
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Francesco
full_name: Montagna, Francesco
id: 353afc8e-19f4-11f0-9db9-811f1723c83f
last_name: Montagna
- first_name: Maximilian T
full_name: Cairney-Leeming, Maximilian T
id: 2214a80c-31f8-11ee-a48d-cf52cc58759b
last_name: Cairney-Leeming
- first_name: Dhanya
full_name: Sridhar, Dhanya
last_name: Sridhar
- first_name: Francesco
full_name: Locatello, Francesco
id: 26cfd52f-2483-11ee-8040-88983bcc06d4
last_name: Locatello
orcid: 0000-0002-4850-0683
citation:
ama: Montagna F, Cairney-Leeming MT, Sridhar D, Locatello F. Demystifying amortized
causal discovery with transformers. Transactions on Machine Learning Research.
2025.
apa: Montagna, F., Cairney-Leeming, M. T., Sridhar, D., & Locatello, F. (2025).
Demystifying amortized causal discovery with transformers. Transactions on
Machine Learning Research. ML Research Press.
chicago: Montagna, Francesco, Maximilian T Cairney-Leeming, Dhanya Sridhar, and
Francesco Locatello. “Demystifying Amortized Causal Discovery with Transformers.”
Transactions on Machine Learning Research. ML Research Press, 2025.
ieee: F. Montagna, M. T. Cairney-Leeming, D. Sridhar, and F. Locatello, “Demystifying
amortized causal discovery with transformers,” Transactions on Machine Learning
Research. ML Research Press, 2025.
ista: Montagna F, Cairney-Leeming MT, Sridhar D, Locatello F. 2025. Demystifying
amortized causal discovery with transformers. Transactions on Machine Learning
Research.
mla: Montagna, Francesco, et al. “Demystifying Amortized Causal Discovery with Transformers.”
Transactions on Machine Learning Research, ML Research Press, 2025.
short: F. Montagna, M.T. Cairney-Leeming, D. Sridhar, F. Locatello, Transactions
on Machine Learning Research (2025).
corr_author: '1'
date_created: 2026-01-04T23:01:35Z
date_published: 2025-12-18T00:00:00Z
date_updated: 2026-01-05T09:54:59Z
day: '18'
ddc:
- '000'
department:
- _id: FrLo
external_id:
arxiv:
- '2405.16924'
file:
- access_level: open_access
checksum: 968c471bb1f682cf823b2d4cadea8a3f
content_type: application/pdf
creator: dernst
date_created: 2026-01-05T09:51:28Z
date_updated: 2026-01-05T09:51:28Z
file_id: '20939'
file_name: 2025_PMLR_Montagna.pdf
file_size: 1030280
relation: main_file
success: 1
file_date_updated: 2026-01-05T09:51:28Z
has_accepted_license: '1'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
publication: Transactions on Machine Learning Research
publication_identifier:
eissn:
- 2835-8856
publication_status: published
publisher: ML Research Press
quality_controlled: '1'
related_material:
link:
- relation: software
url: https://github.com/francescomontagna/learning-to-induce.git
scopus_import: '1'
status: public
title: Demystifying amortized causal discovery with transformers
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2025'
...