Flexible, Non-parametric Modeling Using Regularized Neural Networks

TL;DR

PrAda-net is a neural network approach that automatically adapts its architecture for non-parametric modeling, enabling interpretable additive models without extensive data exploration.

Contribution

It introduces PrAda-net, a neural network that automatically adjusts its size and structure for flexible, interpretable non-parametric modeling with automatic model selection.

Findings

PrAda-net achieves competitive test error compared to other regularization methods.

It effectively identifies important variables and subsets in simulated data.

Demonstrates applicability to complex, heterogeneous real-world data.

Abstract

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.