The random forest (RF) algorithm has become a very popular prediction method for its great flexibility and promising accuracy. In RF, it is conventional to put equal weights on all the base learners (trees) to aggregate their predictions. However, the predictive performances of different trees within the forest can be very different due to the randomization of the embedded bootstrap sampling and feature selection. In this paper, we focus on RF for regression and propose two optimal weighting algorithms, namely the 1 Step Optimal Weighted RF (1step-WRF$_\mathrm{opt}$) and 2 Steps Optimal Weighted RF (2steps-WRF$_\mathrm{opt}$), that combine the base learners through the weights determined by weight choice criteria. Under some regularity conditions, we show that these algorithms are asymptotically optimal in the sense that the resulting squared loss and risk are asymptotically identical to those of the infeasible but best possible model averaging estimator. Numerical studies conducted on real-world data sets indicate that these algorithms outperform the equal-weight forest and two other weighted RFs proposed in existing literature in most cases.

本文提出了一种基于权重优化的随机森林算法，通过极小化预测误差和风险来决定基本学习器的权重，实验结果显示该算法在回归问题上的预测精度优于其他算法。

最优加权随机森林