Two Dimensional Density Estimation using Smooth Invertible Transformations
Methodology
2008-07-16 v1
Abstract
We investigate the problem of estimating a smooth invertible transformation f when observing independent samples X_1, ..., X_n ~ P \circ f, where P is a known measure. We focus on the two dimensional case where P and f are defined on R^2. We present a flexible class of smooth invertible transformations in two dimensions with variational equations for optimizing over the classes, then study the problem of estimating the transformation f by penalized maximum likelihood estimation. We apply our methodology to the case when P \circ f has a density with respect to Lebesgue measure on R^2 and demonstrate improvements over kernel density estimation on three examples.
Cite
@article{arxiv.0807.2275,
title = {Two Dimensional Density Estimation using Smooth Invertible Transformations},
author = {Ethan Anderes and Marc Coram},
journal= {arXiv preprint arXiv:0807.2275},
year = {2008}
}