Spectral Deconfounding for High-Dimensional Sparse Additive Models

Abstract: Many high-dimensional data sets suffer from hidden confounding which affects both the predictors and the response of interest. In such situations, standard regression methods or algorithms lead to biased estimates. This paper substantially extends previous work on spectral deconfounding for high-dimensional linear models to the nonlinear setting and with this, establishes a proof of concept that spectral deconfounding is valid for general nonlinear models. Concretely, we propose an algorithm to estimate high-dimensional sparse additive models in the presence of hidden dense confounding: arguably, this is a simple yet practically useful nonlinear scope. We prove consistency and convergence rates for our method and evaluate it on synthetic data and a genetic data set.