Asymptotic Distributions and Rates of Convergence for Random Forests via Generalized U-statistics
This work addresses a theoretical gap for researchers and practitioners using random forests, offering incremental improvements in asymptotic analysis.
The paper tackles the lack of theoretical understanding of random forests by establishing rates of convergence and asymptotic normality for their predictions, using generalized U-statistics to allow for larger subsample sizes and providing Berry-Esseen bounds to quantify convergence rates based on subsample size and number of trees.
Random forests remain among the most popular off-the-shelf supervised learning algorithms. Despite their well-documented empirical success, however, until recently, few theoretical results were available to describe their performance and behavior. In this work we push beyond recent work on consistency and asymptotic normality by establishing rates of convergence for random forests and other supervised learning ensembles. We develop the notion of generalized U-statistics and show that within this framework, random forest predictions can potentially remain asymptotically normal for larger subsample sizes than previously established. We also provide Berry-Esseen bounds in order to quantify the rate at which this convergence occurs, making explicit the roles of the subsample size and the number of trees in determining the distribution of random forest predictions.