Density Estimation with Distribution Element Trees

TL;DR

This paper introduces a new adaptive density estimation method using distribution elements that efficiently handle high-dimensional data by hierarchical discretization and statistical tests, outperforming existing estimators.

Contribution

The paper presents a novel density estimation approach based on distribution elements with an adaptive hierarchical discretization and a refinement strategy using goodness-of-fit and independence tests.

Findings

Effective in high-dimensional spaces

Outperforms state-of-the-art estimators in experiments

Adaptive discretization improves density approximation

Abstract

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.