IDEAS home Printed from https://ideas.repec.org/a/taf/gnstxx/v24y2012i3p543-562.html
   My bibliography  Save this article

Variance reduction in purely random forests

Author

Listed:
  • Robin Genuer

Abstract

Random forests (RFs), introduced by Leo Breiman in 2001, are a very effective statistical method. The complex mechanism of the method makes theoretical analysis difficult. Therefore, simplified versions of RF, called purely RFs (PRF), which can be theoretically handled more easily, have been considered. In this paper, we study the variance of such forests. First, we show a general upper bound which emphasises the fact that a forest reduces the variance. We then introduce a simple variant of PRFs, that we call purely uniformly RFs. For this variant and in the context of regression problems with a one-dimensional predictor space, we show that both random trees and RFs reach minimax rate of convergence. In addition, we prove that compared with random trees, RFs improve accuracy by reducing the estimator variance by a factor of three-fourths.

Suggested Citation

  • Robin Genuer, 2012. "Variance reduction in purely random forests," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 543-562.
    • Handle: RePEc:taf:gnstxx:v:24:y:2012:i:3:p:543-562
    DOI: 10.1080/10485252.2012.677843
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/10485252.2012.677843
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/10485252.2012.677843?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sylvain Arlot & Robin Genuer, 2016. "Comments 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 228-238, June.
    2. 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.
    3. Zhexiao Lin & Fang Han, 2022. "On regression-adjusted imputation estimators of the average treatment effect," Papers 2212.05424, arXiv.org, revised Jan 2023.
    4. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:gnstxx:v:24:y:2012:i:3:p:543-562. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/GNST20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.