Efficient Deterministic Conditional Sampling of Multivariate Gaussian Densities

Autor

Uwe D. Hanebeck

Korrespondierender Autor

Daniel Frisch

Beteiligtes Institut

Institut für Anthropomatik und Robotik (IAR)

Genre

Veranstaltung

Beschreibung

We propose a fast method for deterministic multi-variate Gaussian sampling. In many application scenarios, the commonly used stochastic Gaussian sampling could simply be replaced by our method – yielding comparable results with a much smaller number of samples. Conformity between the reference Gaussian density function and the distribution of samples is established by minimizing a distance measure between Gaussian density and Dirac mixture density. A modified Cramér-von Mises distance of the Localized Cumulative Distributions (LCDs) of the two densities is employed that allows a direct comparison between continuous and discrete densities in higher dimensions. Because numerical minimization of this distance measure is not feasible under real time constraints, we propose to build a library that maintains sample locations from the standard normal distribution as a template for each number of samples in each dimension. During run time, the requested sample set is re-scaled according to the eigenvalues of the covariance matrix, rotated according to the eigenvectors, and translated according to the mean vector, thus adequately representing arbitrary multivariate normal distributions.

Schlagwörter

deterministic sampling, Gaussian sampling, localized cumulative distribution, transformable sampling

Laufzeit (hh:mm:ss)

00:13:53

Publiziert am

22.04.2026

Fachgebiet

Informatik

Lizenz

KITopen-Lizenz

Aufrufe

6