Efficient Deterministic Conditional Sampling of Multivariate Gaussian Densities

Abstract

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.