Related papers: Sliced Optimal Transport Plans
The Sliced-Wasserstein (SW) distance between probability measures is defined as the average of the Wasserstein distances resulting for the associated one-dimensional projections. As a consequence, the SW distance can be written as an…
We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization…
Optimal transport (OT) is a versatile framework for comparing probability measures, with many applications to statistics, machine learning, and applied mathematics. However, OT distances suffer from computational and statistical scalability…
This note is a continuation of the author's previous work on "Sharp bounds for the max-sliced Wasserstein distance." We use the same technique to obtain an upper bound for the expected max-sliced 2-Wasserstein distance between a compactly…
Optimal transport (OT) distances are increasingly used as loss functions for statistical inference, notably in the learning of generative models or supervised learning. Yet, the behavior of minimum Wasserstein estimators is poorly…
We define a modified Wasserstein distance for distribution clustering which inherits many of the properties of the Wasserstein distance but which can be estimated easily and computed quickly. The modified distance is the sum of two terms.…
Applications of optimal transport have recently gained remarkable attention thanks to the computational advantages of entropic regularization. However, in most situations the Sinkhorn approximation of the Wasserstein distance is replaced by…
Sinkhorn divergence is a measure of dissimilarity between two probability measures. It is obtained through adding an entropic regularization term to Kantorovich's optimal transport problem and can hence be viewed as an entropically…
The Busemann function has recently found much interest in a variety of geometric machine learning problems, as it naturally defines projections onto geodesic rays of Riemannian manifolds and generalizes the notion of hyperplanes. As several…
Projection robust Wasserstein (PRW) distance, or Wasserstein projection pursuit (WPP), is a robust variant of the Wasserstein distance. Recent work suggests that this quantity is more robust than the standard Wasserstein distance, in…
Discrepancy measures between probability distributions, often termed statistical distances, are ubiquitous in probability theory, statistics and machine learning. To combat the curse of dimensionality when estimating these distances from…
Learning an effective representation of 3D point clouds requires a good metric to measure the discrepancy between two 3D point sets, which is non-trivial due to their irregularity. Most of the previous works resort to using the Chamfer…
In the field of modern high-energy physics research, there is a growing emphasis on utilizing deep learning techniques to optimize event simulation, thereby expanding the statistical sample size for more accurate physical analysis.…
We propose a fundamental metric for measuring the distance between two distributions. This metric, referred to as the decision-focused (DF) divergence, is tailored to stochastic linear optimization problems in which the objective…
It was recently shown that under smoothness conditions, the squared Wasserstein distance between two distributions could be efficiently computed with appealing statistical error upper bounds. However, rather than the distance itself, the…
The idea of slicing divergences has been proven to be successful when comparing two probability measures in various machine learning applications including generative modeling, and consists in computing the expected value of a `base…
Sliced Wasserstein (SW) distance has been widely used in different application scenarios since it can be scaled to a large number of supports without suffering from the curse of dimensionality. The value of sliced Wasserstein distance is…
Wasserstein 1 optimal transport maps provide a natural correspondence between points from two probability distributions, $\mu$ and $\nu$, which is useful in many applications. Available algorithms for computing these maps do not appear to…
In this paper we introduce a Wasserstein-type distance on the set of Gaussian mixture models. This distance is defined by restricting the set of possible coupling measures in the optimal transport problem to Gaussian mixture models. We…
This paper will introduce a family of sliced Wasserstein geodesics which are not standard Wasserstein geodesics, objects yet to be discovered in the literature. These objects exhibit how the geometric structure of the Sliced Wasserstein…