Density Estimation with Distribution Element Trees

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 distribution to be estimated 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 high and variable or low densities, respectively. The refinement strategy that we propose is based on statistical goodness-of-fit and 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 low and high-dimensional examples.