Combining additive models and neural networks allows to broaden the scope of
statistical regression and extends deep learning-based approaches by
interpretable structured additive predictors at the same time. Existing
approaches uniting the two modeling approaches are, however, limited to very
specific combinations and, more importantly, involve an identifiability issue.
As a consequence, interpretability and stable estimation is typically lost. We
propose a general framework to combine structured regression models and deep
neural networks into a unifying network architecture. To overcome the inherent
identifiability issues between different model parts, we construct an
orthogonalization cell that projects the deep neural network into the
orthogonal complement of the statistical model predictor. This enables proper
estimation of structured model parts and thereby interpretability. We
demonstrate the framework's efficacy in numerical experiments and illustrate
its special merits in benchmarks and real-world applications