Flexible, non-parametric modeling using regularized neural networks

• Published in: Computational statistics Vol. 37; no. 4; pp. 2029 - 2047
• Main Authors: Allerbo, Oskar, Jörnsten, Rebecka
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2022; Springer Nature B.V
• Subjects: Adaptive lasso; Additive models; Complexity; Economic Theory/Quantitative Economics/Mathematical Methods; Matematik; Mathematics; Mathematics and Statistics; Model selection; Neural networks; Non-parametric regression; Nonparametric statistics; Original Paper; Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Regularization; Spatial data; Statistical models; Statistics; Adaptive lasso; Non-parametric regression; Model selection; Neural networks; Regularization; Additive models
• ISSN: 0943-4062; 1613-9658; 1613-9658
• DOI: 10.1007/s00180-021-01190-4

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 we compare 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.