Spectral Representation Learning for Conditional Moment Models

TL;DR

This paper introduces a spectral representation learning method for conditional moment models that automatically controls ill-posedness, enabling efficient and consistent estimation in causal inference tasks with high-dimensional data.

Contribution

It proposes a novel spectral decomposition approach to learn representations that address ill-posedness in nonparametric conditional moment models, improving estimation efficiency.

Findings

Efficient spectral representation can be learned from data.

The method achieves L2 consistency in estimation.

Promising results on high-dimensional causal inference tasks.

Abstract

Many problems in causal inference and economics can be formulated in the framework of conditional moment models, which characterize the target function through a collection of conditional moment restrictions. For nonparametric conditional moment models, efficient estimation often relies on preimposed conditions on various measures of ill-posedness of the hypothesis space, which are hard to validate when flexible models are used. In this work, we address this issue by proposing a procedure that automatically learns representations with controlled measures of ill-posedness. Our method approximates a linear representation defined by the spectral decomposition of a conditional expectation operator, which can be used for kernelized estimators and is known to facilitate minimax optimal estimation in certain settings. We show this representation can be efficiently estimated from data, and establish L2 consistency for the resulting estimator. We evaluate the proposed method on proximal causal inference tasks, exhibiting promising performance on high-dimensional, semi-synthetic data.