论文标题
半结构化分布回归 - 通过任意深层神经网络和数据模式扩展结构化添加剂模型
Semi-Structured Distributional Regression -- Extending Structured Additive Models by Arbitrary Deep Neural Networks and Data Modalities
论文作者
论文摘要
结合添加剂模型和神经网络允许扩大统计回归的范围，并同时通过可解释的结构化添加剂预测变量扩展基于深度学习的方法。但是，将两种建模方法统一的现有尝试仅限于非常具体的组合，更重要的是涉及可识别性问题。结果，通常会丢失可解释性和稳定的估计。我们提出了一个通用框架，将结构化回归模型和深层神经网络组合到统一的网络体系结构中。为了克服不同模型零件之间固有的可识别性问题，我们构建了一个正交的单元，该细胞将深层神经网络投射到统计模型预测因子的正交补体中。这可以正确估计结构化模型零件，从而可以解释。我们演示了该框架在数值实验中的功效，并在基准和现实世界应用中说明了其特殊优点。
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.
