Measuring the Algorithmic Convergence of Randomized Ensembles: The Regression Setting
This work provides a practical tool for practitioners in machine learning to ensure ensemble convergence in regression, though it is incremental as it extends prior classification work to regression.
The paper tackles the problem of determining when randomized ensembles like bagging and random forests are large enough to approximate an infinite ensemble in regression, proposing a bootstrap method with theoretical guarantees under weak assumptions and demonstrating its effectiveness in variable selection and numerical experiments.
When randomized ensemble methods such as bagging and random forests are implemented, a basic question arises: Is the ensemble large enough? In particular, the practitioner desires a rigorous guarantee that a given ensemble will perform nearly as well as an ideal infinite ensemble (trained on the same data). The purpose of the current paper is to develop a bootstrap method for solving this problem in the context of regression --- which complements our companion paper in the context of classification (Lopes 2019). In contrast to the classification setting, the current paper shows that theoretical guarantees for the proposed bootstrap can be established under much weaker assumptions. In addition, we illustrate the flexibility of the method by showing how it can be adapted to measure algorithmic convergence for variable selection. Lastly, we provide numerical results demonstrating that the method works well in a range of situations.