Fitting deep neural networks into the statistical regression modelling setting

The deep neural network (DNN) model can be viewed as a highly non-linear and semi-parametric generalization of statistical regression models such as the generalized linear model (GLM). The fitting (i.e. learning) of DNN models using training data is usually implemented by minimizing a squared loss function, which is equivalent to a Gaussian likelihood. We present how to understand and fit the DNN models via the GLM framework, with simulated and real data analyses, which are useful for examining the behavior of the GLM-based DNN. Furthermore, we extend the GLM-based DNN to Cox’s proportional hazards models with censored survival data, including an numerical study. The Appendix provides Python codes for a TensorFlow-Keras implementation so that a GLM-based DNN becomes directly accessible to interested readers, including the codes of Cox-based DNN.