Semi-Structured Distributional Regression -- Extending Structured Additive Models by Arbitrary Deep Neural Networks and Data Modalities

arXiv (Cornell University)

Abstract

Combining additive models and neural networks allows to broaden the scope of statistical regression and extend deep learning-based approaches by interpretable structured additive predictors at the same time. Existing attempts 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 are 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.

Authors 3

1. David Rügamer Aachen Institute of Statistics

   RWTH Aachen University · Ludwig-Maximilians-Universität München

   Affiliation as printed

   Department of Statistics , LMU Munich

   Institute of Statistics , RWTH Aachen

2. Chris Kolb

   Ludwig-Maximilians-Universität München

   Affiliation as printed

   Department of Statistics , LMU Munich

3. Nadja Klein

   Humboldt-Universität zu Berlin

   Affiliation as printed

   Chair of Statistics and Data Science , Humboldt-Universität zu Berlin