Decision Forests Induce Characteristic Kernels

Decision forests are popular tools for classification and regression. These forests naturally produce proximity matrices measuring how often each pair of observations lies in the same leaf node. Recently it has been demonstrated that these proximity matrices can be thought of as kernels, connecting the decision forest literature to the extensive kernel machine literature. While other kernels are known to have strong theoretical properties, such as being characteristic kernels, no similar result is available for any decision forest based kernel. We show that a decision forest induced proximity can be made into a characteristic kernel, which can be used within an independence test to obtain a universally consistent test. We therefore empirically evaluate this kernel on a suite of 12 high-dimensional independence test settings: the decision forest induced kernel is shown to typically achieve substantially higher power than other methods.