  Non-parametric, additive models are able to capture complex data dependencies
in a flexible, yet interpretable way. However, choosing the format of the
additive components often requires non-trivial data exploration. Here, as an
alternative, we propose PrAda-net, a one-hidden-layer neural network, trained
with proximal gradient descent and adaptive lasso. PrAda-net automatically
adjusts the size and architecture of the neural network to reflect the
complexity and structure of the data. The compact network obtained by PrAda-net
can be translated to additive model components, making it suitable for
non-parametric statistical modelling with automatic model selection. We
demonstrate PrAda-net on simulated data, where wecompare the test error
performance, variable importance and variable subset identification properties
of PrAda-net to other lasso-based regularization approaches for neural
networks. We also apply PrAda-net to the massive U.K. black smoke data set, to
demonstrate how PrAda-net can be used to model complex and heterogeneous data
with spatial and temporal components. In contrast to classical, statistical
non-parametric approaches, PrAda-net requires no preliminary modeling to select
the functional forms of the additive components, yet still results in an
interpretable model representation.
