Functional Generalized Empirical Likelihood Estimation for Conditional Moment Restrictions

Heiner Kremer, Jia-Jie Zhu, Krikamol Muandet, Bernhard Schölkopf
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:11665-11682, 2022.

Abstract

Important problems in causal inference, economics, and, more generally, robust machine learning can be expressed as conditional moment restrictions, but estimation becomes challenging as it requires solving a continuum of unconditional moment restrictions. Previous works addressed this problem by extending the generalized method of moments (GMM) to continuum moment restrictions. In contrast, generalized empirical likelihood (GEL) provides a more general framework and has been shown to enjoy favorable small-sample properties compared to GMM-based estimators. To benefit from recent developments in machine learning, we provide a functional reformulation of GEL in which arbitrary models can be leveraged. Motivated by a dual formulation of the resulting infinite dimensional optimization problem, we devise a practical method and explore its asymptotic properties. Finally, we provide kernel- and neural network-based implementations of the estimator, which achieve state-of-the-art empirical performance on two conditional moment restriction problems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-kremer22a, title = {Functional Generalized Empirical Likelihood Estimation for Conditional Moment Restrictions}, author = {Kremer, Heiner and Zhu, Jia-Jie and Muandet, Krikamol and Sch{\"o}lkopf, Bernhard}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {11665--11682}, 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/kremer22a/kremer22a.pdf}, url = {https://proceedings.mlr.press/v162/kremer22a.html}, abstract = {Important problems in causal inference, economics, and, more generally, robust machine learning can be expressed as conditional moment restrictions, but estimation becomes challenging as it requires solving a continuum of unconditional moment restrictions. Previous works addressed this problem by extending the generalized method of moments (GMM) to continuum moment restrictions. In contrast, generalized empirical likelihood (GEL) provides a more general framework and has been shown to enjoy favorable small-sample properties compared to GMM-based estimators. To benefit from recent developments in machine learning, we provide a functional reformulation of GEL in which arbitrary models can be leveraged. Motivated by a dual formulation of the resulting infinite dimensional optimization problem, we devise a practical method and explore its asymptotic properties. Finally, we provide kernel- and neural network-based implementations of the estimator, which achieve state-of-the-art empirical performance on two conditional moment restriction problems.} }
Endnote
%0 Conference Paper %T Functional Generalized Empirical Likelihood Estimation for Conditional Moment Restrictions %A Heiner Kremer %A Jia-Jie Zhu %A Krikamol Muandet %A Bernhard Schölkopf %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-kremer22a %I PMLR %P 11665--11682 %U https://proceedings.mlr.press/v162/kremer22a.html %V 162 %X Important problems in causal inference, economics, and, more generally, robust machine learning can be expressed as conditional moment restrictions, but estimation becomes challenging as it requires solving a continuum of unconditional moment restrictions. Previous works addressed this problem by extending the generalized method of moments (GMM) to continuum moment restrictions. In contrast, generalized empirical likelihood (GEL) provides a more general framework and has been shown to enjoy favorable small-sample properties compared to GMM-based estimators. To benefit from recent developments in machine learning, we provide a functional reformulation of GEL in which arbitrary models can be leveraged. Motivated by a dual formulation of the resulting infinite dimensional optimization problem, we devise a practical method and explore its asymptotic properties. Finally, we provide kernel- and neural network-based implementations of the estimator, which achieve state-of-the-art empirical performance on two conditional moment restriction problems.
APA
Kremer, H., Zhu, J., Muandet, K. & Schölkopf, B.. (2022). Functional Generalized Empirical Likelihood Estimation for Conditional Moment Restrictions. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:11665-11682 Available from https://proceedings.mlr.press/v162/kremer22a.html.

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