Projection Pursuit through Relative Entropy Minimization

TL;DR

This paper introduces a new algorithm for Projection Pursuit that utilizes relative entropy minimization to estimate high-dimensional densities and includes a statistical test for density factorization.

Contribution

It presents a novel algorithm based on relative entropy minimization and a test for density factorization, advancing Projection Pursuit methodology.

Findings

New algorithm for density estimation in high dimensions

Statistical test for density factorization introduced

Improved understanding of density structure through entropy minimization

Abstract

Projection Pursuit methodology permits to solve the difficult problem of finding an estimate of a density defined on a set of very large dimension. In his seminal article, Huber (see "Projection pursuit", Annals of Statistics, 1985) evidences the interest of the Projection Pursuit method thanks to the factorisation of a density into a Gaussian component and some residual density in a context of Kullback-Leibler divergence maximisation. In the present article, we introduce a new algorithm, and in particular a test for the factorisation of a density estimated from an iid sample.