Learning Causal Models from Conditional Moment Restrictions by Importance Weighting

TL;DR

This paper introduces a method to learn causal models from conditional moment restrictions by transforming them into unconditional restrictions via importance weighting, enabling effective estimation in high-dimensional settings.

Contribution

The paper proposes a novel importance weighting approach to handle conditional moment restrictions for causal inference, applicable to neural networks and providing theoretical error analysis.

Findings

Effective transformation from conditional to unconditional moment restrictions

Successful nonparametric function estimation under complex restrictions

Theoretical error bounds support the method's validity

Abstract

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.