Title: Outcome-Aware Spectral Feature Learning for Instrumental Variable Regression
Primary area: learning theory
Keywords: instrumental variable regression, NPIV, nonparametric statistics, feature learning, causal inference, operator learning

Abstract: We address the problem of causal effect estimation in the presence of hidden confounders using nonparametric instrumental variable (IV) regression. An established approach is to use estimators based on learned \emph{spectral features}, that is, features spanning the top singular subspaces of the operator linking treatments to instruments. While powerful, such features are agnostic to the outcome variable. Consequently, the method can fail when the true causal function is poorly represented by these dominant singular functions.

To mitigate, we introduce **Augmented Spectral Feature Learning**, a framework that makes the feature learning process **outcome-aware**. Our method learns features by minimizing a novel contrastive loss derived from an **augmented** operator that incorporates information from the outcome. By learning these task-specific features, our approach remains effective even under spectral misalignment. We provide a theoretical analysis of this framework and validate our approach on challenging benchmarks.