Density Estimation with Distribution Element Trees
This addresses the need for scalable density estimation in statistical applications, though it appears incremental as it builds on existing concepts with a novel refinement strategy.
The authors tackled the problem of computationally efficient density estimation for large or high-dimensional datasets by proposing a new method based on distribution elements, which adaptively discretizes the sample space and was successfully compared to state-of-the-art estimators in various examples.
The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient methods are needed. We propose a new method that is based on a decomposition of the unknown distribution in terms of so-called distribution elements (DEs). These elements enable an adaptive and hierarchical discretization of the sample space with small or large elements in regions with smoothly or highly variable densities, respectively. The novel refinement strategy that we propose is based on statistical goodness-of-fit and pair-wise (as an approximation to mutual) independence tests that evaluate the local approximation of the distribution in terms of DEs. The capabilities of our new method are inspected based on several examples of different dimensionality and successfully compared with other state-of-the-art density estimators.