  Many high-dimensional data sets suffer from hidden confounding. When hidden
confounders affect both the predictors and the response in a high-dimensional
regression problem, standard methods 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 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.
