Exploiting Independent Instruments: Identification and Distribution Generalization

Sorawit Saengkyongam, Leonard Henckel, Niklas Pfister, Jonas Peters
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:18935-18958, 2022.

Abstract

Instrumental variable models allow us to identify a causal function between covariates $X$ and a response $Y$, even in the presence of unobserved confounding. Most of the existing estimators assume that the error term in the response $Y$ and the hidden confounders are uncorrelated with the instruments $Z$. This is often motivated by a graphical separation, an argument that also justifies independence. Positing an independence restriction, however, leads to strictly stronger identifiability results. We connect to the existing literature in econometrics and provide a practical method called HSIC-X for exploiting independence that can be combined with any gradient-based learning procedure. We see that even in identifiable settings, taking into account higher moments may yield better finite sample results. Furthermore, we exploit the independence for distribution generalization. We prove that the proposed estimator is invariant to distributional shifts on the instruments and worst-case optimal whenever these shifts are sufficiently strong. These results hold even in the under-identified case where the instruments are not sufficiently rich to identify the causal function.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-saengkyongam22a, title = {Exploiting Independent Instruments: Identification and Distribution Generalization}, author = {Saengkyongam, Sorawit and Henckel, Leonard and Pfister, Niklas and Peters, Jonas}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {18935--18958}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/saengkyongam22a/saengkyongam22a.pdf}, url = {https://proceedings.mlr.press/v162/saengkyongam22a.html}, abstract = {Instrumental variable models allow us to identify a causal function between covariates $X$ and a response $Y$, even in the presence of unobserved confounding. Most of the existing estimators assume that the error term in the response $Y$ and the hidden confounders are uncorrelated with the instruments $Z$. This is often motivated by a graphical separation, an argument that also justifies independence. Positing an independence restriction, however, leads to strictly stronger identifiability results. We connect to the existing literature in econometrics and provide a practical method called HSIC-X for exploiting independence that can be combined with any gradient-based learning procedure. We see that even in identifiable settings, taking into account higher moments may yield better finite sample results. Furthermore, we exploit the independence for distribution generalization. We prove that the proposed estimator is invariant to distributional shifts on the instruments and worst-case optimal whenever these shifts are sufficiently strong. These results hold even in the under-identified case where the instruments are not sufficiently rich to identify the causal function.} }
Endnote
%0 Conference Paper %T Exploiting Independent Instruments: Identification and Distribution Generalization %A Sorawit Saengkyongam %A Leonard Henckel %A Niklas Pfister %A Jonas Peters %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-saengkyongam22a %I PMLR %P 18935--18958 %U https://proceedings.mlr.press/v162/saengkyongam22a.html %V 162 %X Instrumental variable models allow us to identify a causal function between covariates $X$ and a response $Y$, even in the presence of unobserved confounding. Most of the existing estimators assume that the error term in the response $Y$ and the hidden confounders are uncorrelated with the instruments $Z$. This is often motivated by a graphical separation, an argument that also justifies independence. Positing an independence restriction, however, leads to strictly stronger identifiability results. We connect to the existing literature in econometrics and provide a practical method called HSIC-X for exploiting independence that can be combined with any gradient-based learning procedure. We see that even in identifiable settings, taking into account higher moments may yield better finite sample results. Furthermore, we exploit the independence for distribution generalization. We prove that the proposed estimator is invariant to distributional shifts on the instruments and worst-case optimal whenever these shifts are sufficiently strong. These results hold even in the under-identified case where the instruments are not sufficiently rich to identify the causal function.
APA
Saengkyongam, S., Henckel, L., Pfister, N. & Peters, J.. (2022). Exploiting Independent Instruments: Identification and Distribution Generalization. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:18935-18958 Available from https://proceedings.mlr.press/v162/saengkyongam22a.html.

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