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Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction
Afsaneh Mastouri · Yuchen Zhu · Limor Gultchin · Anna Korba · Ricardo Silva · Matt J. Kusner · Arthur Gretton · Krikamol Muandet

Wed Jul 21 07:40 AM -- 07:45 AM (PDT) @

We address the problem of causal effect estima-tion in the presence of unobserved confounding,but where proxies for the latent confounder(s) areobserved. We propose two kernel-based meth-ods for nonlinear causal effect estimation in thissetting: (a) a two-stage regression approach, and(b) a maximum moment restriction approach. Wefocus on the proximal causal learning setting, butour methods can be used to solve a wider classof inverse problems characterised by a Fredholmintegral equation. In particular, we provide a uni-fying view of two-stage and moment restrictionapproaches for solving this problem in a nonlin-ear setting. We provide consistency guaranteesfor each algorithm, and demonstrate that these ap-proaches achieve competitive results on syntheticdata and data simulating a real-world task. In par-ticular, our approach outperforms earlier methodsthat are not suited to leveraging proxy variables.

Author Information

Afsaneh Mastouri (University College London)
Yuchen Zhu (University College London)
Limor Gultchin (University of Oxford)
Anna Korba (CREST/ENSAE)
Ricardo Silva (University College London)
Matt J. Kusner (University College London)
Arthur Gretton (Gatsby Computational Neuroscience Unit)
Krikamol Muandet (Max Planck Institute for Intelligent Systems)

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