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We consider learning causal relationships under conditional momentrestrictions. Unlike causal inference under unconditional moment restrictions,conditional moment restrictions pose serious challenges for causal inference,especially in high-dimensional settings. To address this issue, we propose amethod that transforms conditional moment restrictions to unconditional momentrestrictions through importance weighting, using a conditional density ratioestimator. Using this transformation, we successfully estimate nonparametricfunctions defined under conditional moment restrictions. Our proposed frameworkis general and can be applied to a wide range of methods, including neuralnetworks. We analyze the estimation error, providing theoretical support forour proposed method. In experiments, we confirm the soundness of our proposedmethod.

Learning Causal Models from Conditional Moment Restrictions by Importance Weighting