Semi-Structured Distributional Regression -- Extending Structured Additive Models by Arbitrary Deep Neural Networks and Data Modalities
This work addresses the challenge of integrating interpretable statistical models with flexible deep learning for researchers and practitioners in machine learning and statistics, though it is incremental as it builds on existing attempts by solving a specific limitation.
The paper tackles the problem of combining interpretable structured additive models with deep neural networks while avoiding identifiability issues that compromise interpretability and stable estimation. The result is a framework that uses an orthogonalization cell to project neural networks into the orthogonal complement of statistical predictors, demonstrated as effective in benchmarks and real-world applications.
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.