title: Search for the smallest random forest.
abstract: Random forests have emerged as one of the most commonly used nonparametric statistical methods in many scientific areas, particularly in analysis of high throughput genomic data. A general practice in using random forests is to generate a sufficiently large number of trees, although it is subjective as to how large is sufficient. Furthermore, random forests are viewed as "black-box" because of its sheer size. In this work, we address a fundamental issue in the use of random forests: how large does a random forest have to be? To this end, we propose a specific method to find a sub-forest (e.g., in a single digit number of trees) that can achieve the prediction accuracy of a large random forest (in the order of thousands of trees). We tested it on extensive simulation studies and a real study on prognosis of breast cancer. The results show that such sub-forests usually exist and most of them are very small, suggesting they are actually the "representatives" of the whole random forests. We conclude that the sub-forests are indeed the core of a random forest. Thus it is not necessary to use the whole forest for satisfying prediction performance. Also, by reducing the size of a random forest to a manageable size, the random forest is no longer a black-box.
authors.affiliation: Department of Epidemiology and Public Health, Yale University School of Medicine, New Haven, CT 06520-8034, USA, E-mail address:
authors.forename: Heping
authors.initials: H
authors.lastname: Zhang
authors.forename: Minghui
authors.initials: M
authors.lastname: Wang