Scalable Estimation for Structured Additive Distributional Regression

Abstract: Recently, fitting probabilistic models have gained importance in many areas but estimation of such distributional models with very large data sets is a difficult task. In particular, the use of rather complex models can easily lead to memory-related efficiency problems that can make estimation infeasible even on high-performance computers. We therefore propose a novel backfitting algorithm, which is based on the ideas of stochastic gradient descent and can deal virtually with any amount of data on a conventional laptop. The algorithm performs automatic selection of variables and smoothing parameters, and its performance is in most cases superior or at least equivalent to other implementations for structured additive distributional regression, e.g., gradient boosting, while maintaining low computation time. Performance is evaluated using an extensive simulation study and an exceptionally challenging and unique example of lightning count prediction over Austria. A very large dataset with over 9 million observations and 80 covariates is used, so that a prediction model cannot be estimated with standard distributional regression methods but with our new approach.