  Decision forests, including Random Forests and Gradient Boosting Trees, have
recently demonstrated state-of-the-art performance in a variety of machine
learning settings. Decision forests are typically ensembles of axis-aligned
decision trees; that is, trees that split only along feature dimensions. In
contrast, many recent extensions to decision forests are based on axis-oblique
splits. Unfortunately, these extensions forfeit one or more of the favorable
properties of decision forests based on axis-aligned splits, such as robustness
to many noise dimensions, interpretability, or computational efficiency. We
introduce yet another decision forest, called "Sparse Projection Oblique
Randomer Forests" (SPORF). SPORF uses very sparse random projections, i.e.,
linear combinations of a small subset of features. SPORF significantly improves
accuracy over existing state-of-the-art algorithms on a standard benchmark
suite for classification with >100 problems of varying dimension, sample size,
and number of classes. To illustrate how SPORF addresses the limitations of
both axis-aligned and existing oblique decision forest methods, we conduct
extensive simulated experiments. SPORF typically yields improved performance
over existing decision forests, while mitigating computational efficiency and
scalability and maintaining interpretability. SPORF can easily be incorporated
into other ensemble methods such as boosting to obtain potentially similar
gains.
