  Additive models play an essential role in studying non-linear relationships.
Despite many recent advances in estimation, there is a lack of methods and
theories for inference in high-dimensional additive models, including
confidence interval construction and hypothesis testing. Motivated by inference
for non-linear treatment effects, we consider the high-dimensional additive
model and make inference for the derivative of the function of interest. We
propose a novel decorrelated local linear estimator and establish its
asymptotic normality. The main novelty is the construction of the decorrelation
weights, which is instrumental in reducing the error inherited from estimating
the nuisance functions in the high-dimensional additive model. We construct the
confidence interval for the function derivative and conduct the related
hypothesis testing. We demonstrate our proposed method over large-scale
simulation studies and apply it to identify non-linear effects in the motif
regression problem. Our proposed method is implemented in the R package
\texttt{DLL} available from CRAN.
