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Kernel Instrumental Variable Regression

Singh, R; Sahani, M; Gretton, A; (2019) Kernel Instrumental Variable Regression. In: Wallach, H and Larochelle, H and Beygelzimer, A and d'Alché-Buc, F and Fox, E and Garnett., R, (eds.) Proceedings of Advances in Neural Information Processing Systems 32 (NIPS 2019). NIPS Proceedings Green open access

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Abstract

Instrumental variable (IV) regression is a strategy for learning causal relationships in observational data. If measurements of input X and output Y are confounded, the causal relationship can nonetheless be identified if an instrumental variable Z is available that influences X directly, but is conditionally independent of Y given X and the unmeasured confounder. The classic two-stage least squares algorithm (2SLS) simplifies the estimation problem by modeling all relationships as linear functions. We propose kernel instrumental variable regression (KIV), a nonparametric generalization of 2SLS, modeling relations among X, Y , and Z as nonlinear functions in reproducing kernel Hilbert spaces (RKHSs). We prove the consistency of KIV under mild assumptions, and derive conditions under which convergence occurs at the minimax optimal rate for unconfounded, single-stage RKHS regression. In doing so, we obtain an efficient ratio between training sample sizes used in the algorithm’s first and second stages. In experiments, KIV outperforms state of the art alternatives for nonparametric IV regression.

Type: Proceedings paper
Title: Kernel Instrumental Variable Regression
Event: Advances in Neural Information Processing Systems 32 (NIPS 2019)
Open access status: An open access version is available from UCL Discovery
Publisher version: https://papers.nips.cc/paper/8708-kernel-instrumen...
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences > Gatsby Computational Neurosci Unit
URI: https://discovery.ucl.ac.uk/id/eprint/10090062
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