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Flexible, non-parametric modeling using regularized neural networks

Allerbo, Oskar, 1985 (author)
Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper, Tillämpad matematik och statistik,Department of Mathematical Sciences, Applied Mathematics and Statistics,Chalmers tekniska högskola,Chalmers University of Technology,University of Gothenburg,University of Gothenburg and Chalmers University of Technology, Gothenburg, Sweden
Jörnsten, Rebecka, 1971 (author)
Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,University of Gothenburg,Chalmers tekniska högskola,Chalmers University of Technology,University of Gothenburg and Chalmers University of Technology, Gothenburg, Sweden
 (creator_code:org_t)
2022-01-07
2022
English.
In: Computational Statistics. - : Springer Science and Business Media LLC. - 0943-4062 .- 1613-9658. ; 37:4, s. 2029-2047
  • Journal article (peer-reviewed)
Abstract Subject headings
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  • 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. © 2021, The Author(s).

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)
NATURAL SCIENCES  -- Mathematics (hsv//eng)
NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)
NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)
NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

Keyword

Adaptive lasso
Additive models
Model selection
Neural networks
Non-parametric regression
Regularization
Additive models

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