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Spectral Representation Learning for Conditional Moment Models

Ziyu WangYucen LuoYueru LiJun ZhuBernhard Sch\"olkopf
Oct 2022
摘要
Many problems in causal inference and economics can be formulated in theframework of conditional moment models, which characterize the target functionthrough a collection of conditional moment restrictions. For nonparametricconditional moment models, efficient estimation has always relied on preimposedconditions on various measures of ill-posedness of the hypothesis space, whichare hard to validate when flexible models are used. In this work, we addressthis issue by proposing a procedure that automatically learns representationswith controlled measures of ill-posedness. Our method approximates a linearrepresentation defined by the spectral decomposition of a conditionalexpectation operator, which can be used for kernelized estimators and is knownto facilitate minimax optimal estimation in certain settings. We show thisrepresentation can be efficiently estimated from data, and establish L2consistency for the resulting estimator. We evaluate the proposed method onproximal causal inference tasks, exhibiting promising performance onhigh-dimensional, semi-synthetic data.
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