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Neural Random Forests

Author

Listed:
  • Gérard Biau

    (Sorbonne Université, CNRS, LPSM)

  • Erwan Scornet

    (Centre de Mathématiques Appliquées, Ecole Polytechnique, CNRS)

  • Johannes Welbl

    (University College London)

Abstract

Given an ensemble of randomized regression trees, it is possible to restructure them as a collection of multilayered neural networks with particular connection weights. Following this principle, we reformulate the random forest method of Breiman (2001) into a neural network setting, and in turn propose two new hybrid procedures that we call neural random forests. Both predictors exploit prior knowledge of regression trees for their architecture, have less parameters to tune than standard networks, and less restrictions on the geometry of the decision boundaries than trees. Consistency results are proved, and substantial numerical evidence is provided on both synthetic and real data sets to assess the excellent performance of our methods in a large variety of prediction problems.

Suggested Citation

  • Gérard Biau & Erwan Scornet & Johannes Welbl, 2019. "Neural Random Forests," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 347-386, December.
    • Handle: RePEc:spr:sankha:v:81:y:2019:i:2:d:10.1007_s13171-018-0133-y
    DOI: 10.1007/s13171-018-0133-y
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    References listed on IDEAS

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    1. Redmond, Michael & Baveja, Alok, 2002. "A data-driven software tool for enabling cooperative information sharing among police departments," European Journal of Operational Research, Elsevier, vol. 141(3), pages 660-678, September.
    2. Gérard Biau & Erwan Scornet, 2016. "A random forest guided tour," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 197-227, June.
    3. Gérard Biau & Erwan Scornet, 2016. "Rejoinder on: A random forest guided tour," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 264-268, June.
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