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 generalization error of a forest of tree classifiers depends on the strength of the...

We introduce random survival forests, a random forests method for the analysis of right-censored survival data. New survival splitting rules for growing survival trees are introduced, as is a new missing data algorithm for imputing missing data. A conservation-of-events principle for survival forests is introduced and used to define ensemble mortality, a simple interpretable measure of mortalit...

We develop a novel supervised learning/classification method, called disjunctive normal random forest (DNRF). A DNRF is an ensemble of randomly trained disjunctive normal decision trees (DNDT). To construct a DNDT, we formulate each decision tree in the random forest as a disjunction of rules, which are conjunctions of Boolean functions. We then approximate this disjunction of conjunctions with...

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 ∑

This paper proposes a novel type of random forests called a denoising random forests that are robust against noises contained in test samples. Such noise-corrupted samples cause serious damage to the estimation performances of random forests, since unexpected child nodes are often selected and the leaf nodes that the input sample reaches are sometimes far from those for a clean sample. Our main...

Random forests have emerged as a versatile and highly accurate classification and regression methodology, requiring little tuning and providing interpretable outputs. Here, we briefly outline the genesis of, and motivation for, the random forest paradigm as an outgrowth from earlier tree-structured techniques. We elaborate on aspects of prediction error and attendant tuning parameter issues. Ho...

We introduce random survival forests, a random forests method for the analysis of right-censored survival data. New survival splitting rules for growing survival trees are introduced, as is a new missing data algorithm for imputing missing data. A conservation-of-events principle for survival forests is introduced and used to define ensemble mortality, a simple interpretable measure of mortalit...

Spatially Coherent Random Forest (SCRF) extends Random Forest to create spatially coherent labeling. Each split function in SCRF is evaluated based on a traditional information gain measure that is regularized by a spatial coherency term. This way, SCRF is encouraged to choose split functions that cluster pixels both in appearance space and in image space. In particular, we use SCRF to detect c...

Random forests are one of the most successful ensemble methods which exhibits performance on the level of boosting and support vector machines. The method is fast, robust to noise, does not overfit and offers possibilities for explanation and visualization of its output. We investigate some possibilities to increase strength or decrease correlation of individual trees in the forest. Using sever...

Random forests are a type of ensemble method which makes predictions by combining the results of several independent trees. However, the theory of random forests has long been outpaced by their application. In this paper, we propose a novel random forests algorithm based on cooperative game theory. Banzhaf power index is employed to evaluate the power of each feature by traversing possible feat...