Spectral Representation for Causal Estimation with Hidden Confounders

Haotian Sun, Antoine Moulin, Tongzheng Ren, Arthur Gretton, Bo Dai
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:2719-2727, 2025.

Abstract

We study the problem of causal effect estimation in the presence of unobserved confounders, focusing on two settings: instrumental variable (IV) regression with additional observed confounders, and proxy causal learning. Our approach uses a singular value decomposition of a conditional expectation operator combined with a saddle-point optimization method. In the IV regression setting, this can be viewed as a neural network generalization of the seminal approach due to Darolles et al. (2011). Saddle-point formulations have recently gained attention because they mitigate the double-sampling bias and are compatible with modern function approximation methods. We provide experimental validation across various settings and show that our approach outperforms existing methods on common benchmarks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-sun25d, title = {Spectral Representation for Causal Estimation with Hidden Confounders}, author = {Sun, Haotian and Moulin, Antoine and Ren, Tongzheng and Gretton, Arthur and Dai, Bo}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {2719--2727}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/sun25d/sun25d.pdf}, url = {https://proceedings.mlr.press/v258/sun25d.html}, abstract = {We study the problem of causal effect estimation in the presence of unobserved confounders, focusing on two settings: instrumental variable (IV) regression with additional observed confounders, and proxy causal learning. Our approach uses a singular value decomposition of a conditional expectation operator combined with a saddle-point optimization method. In the IV regression setting, this can be viewed as a neural network generalization of the seminal approach due to Darolles et al. (2011). Saddle-point formulations have recently gained attention because they mitigate the double-sampling bias and are compatible with modern function approximation methods. We provide experimental validation across various settings and show that our approach outperforms existing methods on common benchmarks.} }
Endnote
%0 Conference Paper %T Spectral Representation for Causal Estimation with Hidden Confounders %A Haotian Sun %A Antoine Moulin %A Tongzheng Ren %A Arthur Gretton %A Bo Dai %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-sun25d %I PMLR %P 2719--2727 %U https://proceedings.mlr.press/v258/sun25d.html %V 258 %X We study the problem of causal effect estimation in the presence of unobserved confounders, focusing on two settings: instrumental variable (IV) regression with additional observed confounders, and proxy causal learning. Our approach uses a singular value decomposition of a conditional expectation operator combined with a saddle-point optimization method. In the IV regression setting, this can be viewed as a neural network generalization of the seminal approach due to Darolles et al. (2011). Saddle-point formulations have recently gained attention because they mitigate the double-sampling bias and are compatible with modern function approximation methods. We provide experimental validation across various settings and show that our approach outperforms existing methods on common benchmarks.
APA
Sun, H., Moulin, A., Ren, T., Gretton, A. & Dai, B.. (2025). Spectral Representation for Causal Estimation with Hidden Confounders. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:2719-2727 Available from https://proceedings.mlr.press/v258/sun25d.html.

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