Journal
JOURNAL OF MULTIVARIATE ANALYSIS
Volume 146, Issue -, Pages 72-83Publisher
ELSEVIER INC
DOI: 10.1016/j.jmva.2015.06.009
Keywords
Random forests; Randomization; Consistency; Central limit theorem; Empirical process; Number of trees; q-quantile
Categories
Ask authors/readers for more resources
The last decade has witnessed a growing interest in random forest models which are recognized to exhibit good practical performance, especially in high-dimensional settings. On the theoretical side, however, their predictive power remains largely unexplained, thereby creating a gap between theory and practice. In this paper, we present some asymptotic results on random forests in a regression framework. Firstly, we provide theoretical guarantees to link finite forests used in practice (with a finite number M of trees) to their asymptotic counterparts (with M = infinity). Using empirical process theory, we prove a uniform central limit theorem for a large class of random forest estimates, which holds in particular for Breiman's (2001) original forests. Secondly, we show that infinite forest consistency implies finite forest consistency and thus, we state the consistency of several infinite forests. In particular, we prove that q quantile forests - close in spirit to Breiman's (2001) forests but easier to study - are able to combine inconsistent trees to obtain a final consistent prediction, thus highlighting the benefits of random forests compared to single trees. (C) 2015 Elsevier Inc. All rights reserved.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available