Learning Causal Relationships from Conditional Moment Restrictions by Importance Weighting

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, especially in complex, high-dimensional settings. To address this issue, we propose a method that transforms conditional moment restrictions to unconditional moment restrictions through importance weighting using the 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. In experiments, we confirm the soundness of our proposed method.