UCL Discovery

Abstract

Gaussian distributions lie at the heart of popular tools for capturing structure in high dimensional data. Standard techniques employ as models arbitrary linear transformations of spherical Gaussians. In this paper, we present a simple extension to a class of nonlinear, volume preserving transformations which provides an efficient local description of curvature. The resulting generalized Gaussian models give a simple statistical tool for measuring deviations from multivariate Gaussian distributions. Remarkably, there is a computationally efficient, analytic solution for fitting the parameters of the non-linear models. The power of this approach is demonstrated in a curvature analysis of the Asian foreign exchange market.