Non-iterative Gaussianization

TL;DR

This paper introduces a non-iterative Gaussianization method using copula functions that accurately transforms any continuous multivariate distribution into a Gaussian, outperforming existing methods and applicable to image density estimation.

Contribution

It presents a novel non-iterative Gaussianization strategy based on copula functions that relaxes previous restrictive assumptions and guarantees exact Gaussian transformation.

Findings

The method outperforms Box-Cox and radial Gaussianization in simulations.

Theoretical guarantees ensure exact Gaussianization of continuous multivariate distributions.

Demonstrates application in probability density estimation for image synthesis.

Abstract

In this work, we propose a non-iterative Gaussian transformation strategy based on copula function, which doesn't require some commonly seen restrictive assumptions in the previous studies such as the elliptically symmetric distribution assumption and the linear independent component analysis assumption. Theoretical properties guarantee the proposed strategy can exactly transfer any random variable vector with a continuous multivariate distribution to a variable vector that follows a multivariate Gaussian distribution. Simulation studies also demonstrate the outperformance of such a strategy compared to some other methods like Box-Cox Gaussianization and radial Gaussianization. An application for probability density estimation for image synthesis is also shown.