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AMF: Aggregated Mondrian forests for online learning

Author

Listed:
  • Jaouad Mourtada
  • Stéphane Gaïffas
  • Erwan Scornet

Abstract

Random forest (RF) is one of the algorithms of choice in many supervised learning applications, be it classification or regression. The appeal of such tree‐ensemble methods comes from a combination of several characteristics: a remarkable accuracy in a variety of tasks, a small number of parameters to tune, robustness with respect to features scaling, a reasonable computational cost for training and prediction, and their suitability in high‐dimensional settings. The most commonly used RF variants, however, are ‘offline’ algorithms, which require the availability of the whole dataset at once. In this paper, we introduce AMF, an online RF algorithm based on Mondrian Forests. Using a variant of the context tree weighting algorithm, we show that it is possible to efficiently perform an exact aggregation over all prunings of the trees; in particular, this enables to obtain a truly online parameter‐free algorithm which is competitive with the optimal pruning of the Mondrian tree, and thus adaptive to the unknown regularity of the regression function. Numerical experiments show that AMF is competitive with respect to several strong baselines on a large number of datasets for multi‐class classification.

Suggested Citation

  • Jaouad Mourtada & Stéphane Gaïffas & Erwan Scornet, 2021. "AMF: Aggregated Mondrian forests for online learning," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(3), pages 505-533, July.
    • Handle: RePEc:bla:jorssb:v:83:y:2021:i:3:p:505-533
    DOI: 10.1111/rssb.12425
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    References listed on IDEAS

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    1. Robin Genuer, 2012. "Variance reduction in purely random forests," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 543-562.
    2. Taddy, Matthew A. & Gramacy, Robert B. & Polson, Nicholas G., 2011. "Dynamic Trees for Learning and Design," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 109-123.
    3. Antonio R. Linero & Yun Yang, 2018. "Bayesian regression tree ensembles that adapt to smoothness and sparsity," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(5), pages 1087-1110, November.
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