Discrete mathematics

Random variable

Channel (broadcasting)

Consistency (knowledge bases)

Computer network

Strong consistency

Mathematics

Economic growth

Statistic

Statistics

Random forest

Econometrics

Estimator

Artificial intelligence

Economics

Convergence (economics)

Computer science

Order statistic

Applied mathematics

Convergence of random variables

Rate of convergence

Asymptotic distribution

Electronic Journal of Statistics

Random forests are 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 remain asymptotically normal for larger subsample sizes and under weaker conditions than previously established. Moreover, we 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. When these generalized estimators are reduced to their classical U-statistic form, the rates we establish are faster than any available in the existing literature.

Rates of convergence for random forests via generalized U-statistics