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Brofos, James A; Brubaker, Marcus A; Lederman, Roy R
Manifold Density Estimation via Generalized Dequantization Technical Report
2021, (arXiv: 2102.07143).
Abstract | Links | BibTeX | Tags: Algorithms, Computer Science - Machine Learning, Density estimation, Manifolds, Statistics - Machine Learning
@techreport{brofos_manifold_2021,
title = {Manifold Density Estimation via Generalized Dequantization},
author = {James A Brofos and Marcus A Brubaker and Roy R Lederman},
url = {http://arxiv.org/abs/2102.07143},
year = {2021},
date = {2021-07-01},
urldate = {2021-07-14},
abstract = {Density estimation is an important technique for characterizing distributions given observations. Much existing research on density estimation has focused on cases wherein the data lies in a Euclidean space. However, some kinds of data are not well-modeled by supposing that their underlying geometry is Euclidean. Instead, it can be useful to model such data as lying on a textbackslashit manifold with some known structure. For instance, some kinds of data may be known to lie on the surface of a sphere. We study the problem of estimating densities on manifolds. We propose a method, inspired by the literature on "dequantization," which we interpret through the lens of a coordinate transformation of an ambient Euclidean space and a smooth manifold of interest. Using methods from normalizing flows, we apply this method to the dequantization of smooth manifold structures in order to model densities on the sphere, tori, and the orthogonal group.},
note = {arXiv: 2102.07143},
keywords = {Algorithms, Computer Science - Machine Learning, Density estimation, Manifolds, Statistics - Machine Learning},
pubstate = {published},
tppubtype = {techreport}
}
Density estimation is an important technique for characterizing distributions given observations. Much existing research on density estimation has focused on cases wherein the data lies in a Euclidean space. However, some kinds of data are not well-modeled by supposing that their underlying geometry is Euclidean. Instead, it can be useful to model such data as lying on a textbackslashit manifold with some known structure. For instance, some kinds of data may be known to lie on the surface of a sphere. We study the problem of estimating densities on manifolds. We propose a method, inspired by the literature on "dequantization," which we interpret through the lens of a coordinate transformation of an ambient Euclidean space and a smooth manifold of interest. Using methods from normalizing flows, we apply this method to the dequantization of smooth manifold structures in order to model densities on the sphere, tori, and the orthogonal group.