Learning Causal Models from Conditional Moment Restrictions by Importance Weighting
This work addresses a critical bottleneck in causal inference for high-dimensional data, offering a general framework applicable to methods like neural networks.
The paper tackles the challenge of learning causal relationships under conditional moment restrictions in high-dimensional settings by transforming them into unconditional moment restrictions via importance weighting with a conditional density ratio estimator, successfully estimating nonparametric functions and confirming the method's soundness in experiments.
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 high-dimensional settings. 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. Using this transformation, we successfully estimate nonparametric functions defined under conditional moment restrictions. Our proposed framework is general and can be applied to a wide range of methods, including neural networks. We analyze the estimation error, providing theoretical support for our proposed method. In experiments, we confirm the soundness of our proposed method.