  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.
