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Learning Causal Models from Conditional Moment Restrictions by Importance Weighting

Masahiro Kato · Masaaki Imaizumi · Kenichiro McAlinn · Shota Yasui · Haruo Kakehi

Keywords: [ causal inference ]


We consider learning causal relationships under conditional moment restrictions. Unlike causal inference under unconditional moment restrictions, conditional moment restrictions pose serious challenges for causal inference. To address this issue, we propose a method that transforms conditional moment restrictions to unconditional moment restrictions through importance weighting using a conditional density ratio estimator. Then, using this transformation, we propose a method that successfully estimate a parametric or nonparametric functions defined under the conditional moment restrictions. We analyze the estimation error and provide a bound on the structural function, providing theoretical support for our proposed method. In experiments, we confirm the soundness of our proposed method.

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