Spectrum of Variable-Random Trees

Abstract

In this paper, we show that a continuous spectrum of randomisation exists, in which most existing tree randomisations are only operating around the two ends of the spectrum. That leaves a huge part of the spectrum largely unexplored. We propose a base learner VR-Tree which generates trees with variable-randomness. VR-Trees are able to span from the conventional deterministic trees to the complete-random trees using a probabilistic parameter. Using VR-Trees as the base models, we explore the entire spectrum of randomised ensembles, together with Bagging and Random Subspace. We discover that the two halves of the spectrum have their distinct characteristics; and the understanding of which allows us to propose a new approach in building better decision tree ensembles. We name this approach Coalescence, which coalesces a number of points in the random-half of the spectrum. Coalescence acts as a committee of ``experts'' to cater for unforeseeable conditions presented in training data. Coalescence is found to perform better than any single operating point in the spectrum, without the need to tune to a specific level of randomness. In our empirical study, Coalescence ranks top among the benchmarking ensemble methods including Random Forests, Random Subspace and C5 Boosting; and only Coalescence is significantly better than Bagging and Max-Diverse Ensemble among all the methods in the comparison. Although Coalescence is not significantly better than Random Forests, we have identified conditions under which one will perform better than the other.