Kernel Single Proxy Control for Deterministic Confounding

Liyuan Xu, Arthur Gretton
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:3736-3744, 2025.

Abstract

We consider the problem of causal effect estimation with an unobserved confounder, where we observe a single proxy variable that is associated with the confounder. Although it has been shown that the recovery of an average causal effect is impossible in general from a single proxy variable, we show that causal recovery is possible if the outcome is generated deterministically. This generalizes existing work on causal methods with a single proxy variable to the continuous treatment setting. We propose two kernel-based methods for this setting: the first based on the two-stage regression approach, and the second based on a maximum moment restriction approach. We prove that both approaches can consistently estimate the causal effect, and we empirically demonstrate that we can successfully recover the causal effect on challenging synthetic benchmarks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-xu25g, title = {Kernel Single Proxy Control for Deterministic Confounding}, author = {Xu, Liyuan and Gretton, Arthur}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {3736--3744}, 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/xu25g/xu25g.pdf}, url = {https://proceedings.mlr.press/v258/xu25g.html}, abstract = {We consider the problem of causal effect estimation with an unobserved confounder, where we observe a single proxy variable that is associated with the confounder. Although it has been shown that the recovery of an average causal effect is impossible in general from a single proxy variable, we show that causal recovery is possible if the outcome is generated deterministically. This generalizes existing work on causal methods with a single proxy variable to the continuous treatment setting. We propose two kernel-based methods for this setting: the first based on the two-stage regression approach, and the second based on a maximum moment restriction approach. We prove that both approaches can consistently estimate the causal effect, and we empirically demonstrate that we can successfully recover the causal effect on challenging synthetic benchmarks.} }
Endnote
%0 Conference Paper %T Kernel Single Proxy Control for Deterministic Confounding %A Liyuan Xu %A Arthur Gretton %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-xu25g %I PMLR %P 3736--3744 %U https://proceedings.mlr.press/v258/xu25g.html %V 258 %X We consider the problem of causal effect estimation with an unobserved confounder, where we observe a single proxy variable that is associated with the confounder. Although it has been shown that the recovery of an average causal effect is impossible in general from a single proxy variable, we show that causal recovery is possible if the outcome is generated deterministically. This generalizes existing work on causal methods with a single proxy variable to the continuous treatment setting. We propose two kernel-based methods for this setting: the first based on the two-stage regression approach, and the second based on a maximum moment restriction approach. We prove that both approaches can consistently estimate the causal effect, and we empirically demonstrate that we can successfully recover the causal effect on challenging synthetic benchmarks.
APA
Xu, L. & Gretton, A.. (2025). Kernel Single Proxy Control for Deterministic Confounding. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:3736-3744 Available from https://proceedings.mlr.press/v258/xu25g.html.

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