Independent Elliptical Distributions Minimize Their $\mathcal{W}_2$ Wasserstein Distance from Independent Elliptical Distributions with the Same Density Generator

• URL: http://arxiv.org/abs/2012.03809v1
• Date: Mon, 7 Dec 2020 15:52:02 GMT
• Title: Independent Elliptical Distributions Minimize Their $\mathcal{W}_2$ Wasserstein Distance from Independent Elliptical Distributions with the Same Density Generator
• Authors: Song Fang and Quanyan Zhu
• Abstract summary: This note is on a property of the $mathcalW$ Wasserstein distance. It indicates that independent elliptical distributions minimize their $mathcalW$ Wasserstein distance from given independent elliptical distributions with the same density generators.
• Score: 30.590501280252948
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This short note is on a property of the $\mathcal{W}_2$ Wasserstein distance which indicates that independent elliptical distributions minimize their $\mathcal{W}_2$ Wasserstein distance from given independent elliptical distributions with the same density generators. Furthermore, we examine the implications of this property in the Gelbrich bound when the distributions are not necessarily elliptical. Meanwhile, we also generalize the results to the cases when the distributions are not independent. The primary purpose of this note is for the referencing of papers that need to make use of this property or its implications.

Related papers

• Gaussian-Smoothed Sliced Probability Divergences [15.123608776470077]
  We show that smoothing and slicing preserve the metric property and the weak topology. We also derive other properties, including continuity, of different divergences with respect to the smoothing parameter.
  arXiv  Detail & Related papers  (2024-04-04T07:55:46Z)
• Energy-Based Sliced Wasserstein Distance [47.18652387199418]
  A key component of the sliced Wasserstein (SW) distance is the slicing distribution. We propose to design the slicing distribution as an energy-based distribution that is parameter-free. We then derive a novel sliced Wasserstein metric, energy-based sliced Waserstein (EBSW) distance.
  arXiv  Detail & Related papers  (2023-04-26T14:28:45Z)
• Bounds on Wasserstein distances between continuous distributions using independent samples [0.0]
  We propose a linear combination of plug-in estimators for the squared 2-Wasserstein distance with a reduced bias that decays to zero with the true distance. We apply it to approximately bound from above the 2-Wasserstein distance between the target and current distribution in Markov chain Monte Carlo.
  arXiv  Detail & Related papers  (2022-03-22T11:26:18Z)
• Non-Gaussian Component Analysis via Lattice Basis Reduction [56.98280399449707]
  Non-Gaussian Component Analysis (NGCA) is a distribution learning problem. We provide an efficient algorithm for NGCA in the regime that $A$ is discrete or nearly discrete.
  arXiv  Detail & Related papers  (2021-12-16T18:38:02Z)
• $\alpha$-Geodesical Skew Divergence [5.3556221126231085]
  The asymmetric skew divergence smooths one of the distributions by mixing it, to a degree determined by the parameter $lambda$, with the other distribution. Such divergence is an approximation of the KL divergence that does not require the target distribution to be absolutely continuous with respect to the source distribution.
  arXiv  Detail & Related papers  (2021-03-31T13:27:58Z)
• Independent Gaussian Distributions Minimize the Kullback-Leibler (KL) Divergence from Independent Gaussian Distributions [23.249999313567624]
  This note is on a property of the Kullback-Leibler (KL) divergence. The primary purpose of this note is for the referencing of papers that need to make use of this property entirely or partially.
  arXiv  Detail & Related papers  (2020-11-04T22:05:45Z)
• Linear Optimal Transport Embedding: Provable Wasserstein classification for certain rigid transformations and perturbations [79.23797234241471]
  Discriminating between distributions is an important problem in a number of scientific fields. The Linear Optimal Transportation (LOT) embeds the space of distributions into an $L2$-space. We demonstrate the benefits of LOT on a number of distribution classification problems.
  arXiv  Detail & Related papers  (2020-08-20T19:09:33Z)
• A diffusion approach to Stein's method on Riemannian manifolds [65.36007959755302]
  We exploit the relationship between the generator of a diffusion on $mathbf M$ with target invariant measure and its characterising Stein operator. We derive Stein factors, which bound the solution to the Stein equation and its derivatives. We imply that the bounds for $mathbb Rm$ remain valid when $mathbf M$ is a flat manifold.
  arXiv  Detail & Related papers  (2020-03-25T17:03:58Z)
• Fast and Robust Comparison of Probability Measures in Heterogeneous Spaces [62.35667646858558]
  We introduce the Anchor Energy (AE) and Anchor Wasserstein (AW) distances, which are respectively the energy and Wasserstein distances instantiated on such representations. Our main contribution is to propose a sweep line algorithm to compute AE emphexactly in log-quadratic time, where a naive implementation would be cubic. We show that AE and AW perform well in various experimental settings at a fraction of the computational cost of popular GW approximations.
  arXiv  Detail & Related papers  (2020-02-05T03:09:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.