2019/12/30 by Uwe D. Hanebeck, Hanebeck, Uwe D.
Computer Science · Engineering · Physics and Astronomy · #Control Systems and Identification #FOS: Electrical engineering #Gaussian Processes and Bayesian Inference #Scientific Research and Discoveries #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1912.12875
openalex publication_date 2019/12/30 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
We want to approximate general multivariate probability density functions by\ndeterministic sample sets. For optimal sampling, the closeness to the given\ncontinuous density has to be assessed. This is a difficult challenge in\nmultivariate settings. Simple solutions are restricted to the one-dimensional\ncase. In this paper, we propose to employ one-dimensional density projections.\nThese are the Radon transforms of the densities. For every projection, we\ncompute their cumulative distribution function. These Projected Cumulative\nDistributions (PCDs) are compared for all possible projections (or a discrete\nset thereof). This leads to a tractable distance measure in multivariate space.\nThe proposed approximation method is efficient as calculating the distance\nmeasure mainly entails sorting in one dimension. It is also surprisingly simple\nto implement.\n