Spectral Representation Learning for Conditional Moment Models

• URL: http://arxiv.org/abs/2210.16525v1
• Date: Sat, 29 Oct 2022 07:48:29 GMT
• Title: Spectral Representation Learning for Conditional Moment Models
• Authors: Ziyu Wang, Yucen Luo, Yueru Li, Jun Zhu, Bernhard Sch\"olkopf
• Abstract summary: We propose 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. We show this representation can be efficiently estimated from data, and establish L2 consistency for the resulting estimator.
• Score: 33.34244475589745
• License: http://creativecommons.org/licenses/by/4.0/
• 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 has always relied 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.

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