The Extra-Tree method (standing for extremely randomized trees) was proposed in [GEW06], with the main objective of further randomizing tree building in the context of numerical input features, where the choice of the optimal cut-point is responsible for a large proportion of the variance of the induced tree.
With respect to random forests, the method drops the idea of using bootstrap copies of the learning sample, and instead of trying to find an optimal cut-point for each one of the K randomly chosen features at each node, it selects a cut-point at random.
From a statistical point of view, dropping the bootstrapping idea leads to an advantage in terms of bias, whereas the cut-point randomization has often an excellent variance reduction effect. This method has yielded state-of-the-art results in several high-dimensional complex problems.
From a functional point of view, the Extra-Tree method produces piece-wise multilinear approximations, rather than the piece-wise constant ones of random forests [GEW06].
