Variance reduction in purely random forests

Analysis of purely random forests bias

Random forests are a very effective and commonly used statistical method, but their full theoretical analysis is still an open problem. As a first step, simplified models such as purely random forests have been introduced, in order to shed light on the good performance of random forests. In this paper, we study the approximation error (the bias) of some purely random forest models in a regressi...

Risk bounds for purely uniformly random forests

Random forests, introduced by Leo Breiman in 2001, are a very effective statistical method. The complex mechanism of the method makes theoretical analysis difficult. Therefore, a simplified version of random forests, called purely random forests, which can be theoretically handled more easily, has been considered. In this paper we introduce a variant of this kind of random forests, that we call...

Forests in Random Graphs

Let G be a graph and let I(G) be defined by I(G) = max{|F | : F is an induced forest in G}. Let d = (d1, d2, . . . , dn) be a graphic degree sequence such that d1 ≥ d2 ≥ · · · ≥ dn ≥ 1. By using the probabilistic method, we prove that if G is a graph with degree sequence d, then I(G) ≥ 2 n ∑

Variance Reduction Techniques in . . .

1 Random Forests - - Random Features

Random forests are a combination of tree predictors such that each tree depends on the values of a random vector sampled independently and with the same distribution for all trees in the forest. The generalization error for forests converges a.s. to a limit as the number of trees in the forest becomes large. The error of a forest of tree classifiers depends on the strength of the individual tre...