Causal inference with treatment measurement error: a nonparametric instrumental variable approach

Yuchen Zhu, Limor Gultchin, Arthur Gretton, Matt J. Kusner, Ricardo Silva
Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, PMLR 180:2414-2424, 2022.

Abstract

We propose a kernel-based nonparametric estimator for the causal effect when the cause is corrupted by error. We do so by generalizing estimation in the instrumental variable setting. Despite significant work on regression with measurement error, additionally handling unobserved confounding in the continuous setting is non-trivial: we have seen little prior work. As a by-product of our investigation, we clarify a connection between mean embeddings and characteristic functions, and how learning one simultaneously allows one to learn the other. This opens the way for kernel method research to leverage existing results in characteristic function estimation. Finally, we empirically show that our proposed method, MEKIV, improves over baselines and is robust under changes in the strength of measurement error and to the type of error distributions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v180-zhu22a, title = {Causal inference with treatment measurement error: a nonparametric instrumental variable approach}, author = {Zhu, Yuchen and Gultchin, Limor and Gretton, Arthur and Kusner, Matt J. and Silva, Ricardo}, booktitle = {Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence}, pages = {2414--2424}, year = {2022}, editor = {Cussens, James and Zhang, Kun}, volume = {180}, series = {Proceedings of Machine Learning Research}, month = {01--05 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v180/zhu22a/zhu22a.pdf}, url = {https://proceedings.mlr.press/v180/zhu22a.html}, abstract = {We propose a kernel-based nonparametric estimator for the causal effect when the cause is corrupted by error. We do so by generalizing estimation in the instrumental variable setting. Despite significant work on regression with measurement error, additionally handling unobserved confounding in the continuous setting is non-trivial: we have seen little prior work. As a by-product of our investigation, we clarify a connection between mean embeddings and characteristic functions, and how learning one simultaneously allows one to learn the other. This opens the way for kernel method research to leverage existing results in characteristic function estimation. Finally, we empirically show that our proposed method, MEKIV, improves over baselines and is robust under changes in the strength of measurement error and to the type of error distributions.} }
Endnote
%0 Conference Paper %T Causal inference with treatment measurement error: a nonparametric instrumental variable approach %A Yuchen Zhu %A Limor Gultchin %A Arthur Gretton %A Matt J. Kusner %A Ricardo Silva %B Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2022 %E James Cussens %E Kun Zhang %F pmlr-v180-zhu22a %I PMLR %P 2414--2424 %U https://proceedings.mlr.press/v180/zhu22a.html %V 180 %X We propose a kernel-based nonparametric estimator for the causal effect when the cause is corrupted by error. We do so by generalizing estimation in the instrumental variable setting. Despite significant work on regression with measurement error, additionally handling unobserved confounding in the continuous setting is non-trivial: we have seen little prior work. As a by-product of our investigation, we clarify a connection between mean embeddings and characteristic functions, and how learning one simultaneously allows one to learn the other. This opens the way for kernel method research to leverage existing results in characteristic function estimation. Finally, we empirically show that our proposed method, MEKIV, improves over baselines and is robust under changes in the strength of measurement error and to the type of error distributions.
APA
Zhu, Y., Gultchin, L., Gretton, A., Kusner, M.J. & Silva, R.. (2022). Causal inference with treatment measurement error: a nonparametric instrumental variable approach. Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 180:2414-2424 Available from https://proceedings.mlr.press/v180/zhu22a.html.

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