Instrumental variable regression via kernel maximum moment loss

Zhang Rui (), Imaizumi Masaaki (), Schölkopf Bernhard () and Muandet Krikamol ()
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Zhang Rui: Research School of Computer Science, Australian National University, Canberra ACT 2601, Australia
Imaizumi Masaaki: Komaba Institute for Science (KIS), The University of Tokyo, 7 Chome-3-1 Hongo, Bunkyo City, Tokyo 113-8654, Japan
Schölkopf Bernhard: Empirical Inference Department, Max Planck Institute for Intelligent Systems, Max-Planck-Ring 4, 72076 Tübingen, Germany
Muandet Krikamol: CISPA–Helmholtz Center for Information Security, Saarbrücken, Saarland, Germany

Journal of Causal Inference, 2023, vol. 11, issue 1, 42

Abstract: We investigate a simple objective for nonlinear instrumental variable (IV) regression based on a kernelized conditional moment restriction known as a maximum moment restriction (MMR). The MMR objective is formulated by maximizing the interaction between the residual and the instruments belonging to a unit ball in a reproducing kernel Hilbert space. First, it allows us to simplify the IV regression as an empirical risk minimization problem, where the risk function depends on the reproducing kernel on the instrument and can be estimated by a U-statistic or V-statistic. Second, on the basis this simplification, we are able to provide consistency and asymptotic normality results in both parametric and nonparametric settings. Finally, we provide easy-to-use IV regression algorithms with an efficient hyperparameter selection procedure. We demonstrate the effectiveness of our algorithms using experiments on both synthetic and real-world data.

Keywords: nonlinear instrumental variable regression; conditional moment restriction; kernel method; reproducing kernel Hilbert space; U/V-statistics (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:causin:v:11:y:2023:i:1:p:42:n:1

DOI: 10.1515/jci-2022-0073

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