2016/10/31 by Daniel W. Meyer
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Curse of dimensionality #Density estimation #Discretization #Distribution (mathematics) #Independence (probability theory) #Machine Learning and Algorithms #Mixture distribution #Pairwise comparison #Probability density function #Probability distribution #Statistical Methods and Inference #acm:62G07 #cs.MS #msc:62G07 #stat.CO #stat.ME #stat.ML
paper · pdf · doi:10.1007/s11222-017-9751-9
openalex created_date 2016/10/14 · arxiv created 2017/05/03 · arxiv updated 2017/05/04 · openalex publication_date 2017/05/16 · openalex updated_date 2026/08/05
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.