Spectral Representation for Causal Estimation with Hidden Confounders

We study the problem of causal effect estimation in the presence of unobserved confounders, focusing on two settings: instrumental variable (IV) regression with additional observed confounders, and proxy causal learning. Our approach uses a singular value decomposition of a conditional expectation operator combined with a saddle-point optimization method. In the IV regression setting, this can be viewed as a neural network generalization of the seminal approach due to \cite{darolles2011nonparametric}. Saddle-point formulations have recently gained attention because they mitigate the double-sampling bias and are compatible with modern function approximation methods. We provide experimental validation across various settings and show that our approach outperforms existing methods on common benchmarks.