Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction

• URL: http://arxiv.org/abs/2105.04544v2
• Date: Tue, 11 May 2021 12:29:17 GMT
• Title: Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction
• Authors: Afsaneh Mastouri, Yuchen Zhu, Limor Gultchin, Anna Korba, Ricardo Silva, Matt J. Kusner, Arthur Gretton, Krikamol Muandet
• Abstract summary: We focus on the proximal causal learning setting, but our methods can be used to solve a wider class of inverse problems characterised by a Fredholm integral equation. We provide consistency guarantees for each algorithm, and we demonstrate these approaches achieve competitive results on synthetic data and data simulating a real-world task.
• Score: 39.51144507601913
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We address the problem of causal effect estimation in the presence of unobserved confounding, but where proxies for the latent confounder(s) are observed. We propose two kernel-based methods for nonlinear causal effect estimation in this setting: (a) a two-stage regression approach, and (b) a maximum moment restriction approach. We focus on the proximal causal learning setting, but our methods can be used to solve a wider class of inverse problems characterised by a Fredholm integral equation. In particular, we provide a unifying view of two-stage and moment restriction approaches for solving this problem in a nonlinear setting. We provide consistency guarantees for each algorithm, and we demonstrate these approaches achieve competitive results on synthetic data and data simulating a real-world task. In particular, our approach outperforms earlier methods that are not suited to leveraging proxy variables.

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