Related papers: Revisiting Sliced Wasserstein on Images: From Vect…
Sliced optimal transport (SOT), or sliced Wasserstein (SW) distance, is widely recognized for its statistical and computational scalability. In this work, we further enhance computational scalability by proposing the first method for…
The Wasserstein distance is a distance between two probability distributions and has recently gained increasing popularity in statistics and machine learning, owing to its attractive properties. One important approach to extending this…
Gaussian smoothed sliced Wasserstein distance has been recently introduced for comparing probability distributions, while preserving privacy on the data. It has been shown that it provides performances similar to its non-smoothed…
In this paper, we investigate the properties of the Sliced Wasserstein Distance (SW) when employed as an objective functional. The SW metric has gained significant interest in the optimal transport and machine learning literature, due to…
We develop a projected Wasserstein distance for the two-sample test, a fundamental problem in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. In particular, we aim to…
Spherical Sliced-Wasserstein (SSW) has recently been proposed to measure the discrepancy between spherical data distributions in various fields, such as geology, medical domains, computer vision, and deep representation learning. However,…
Because of the special angular distribution of excited electrons by the photoelectric effect, the Gas Pixel Detector (GPD) is effective in measuring keV X-ray polarization of astrophysical events (e.g. gamma-ray bursts), by capturing…
Optimal Transport (OT) has attracted significant interest in the machine learning community, not only for its ability to define meaningful distances between probability distributions -- such as the Wasserstein distance -- but also for its…
Generative adversarial nets (GANs) and variational auto-encoders have significantly improved our distribution modeling capabilities, showing promise for dataset augmentation, image-to-image translation and feature learning. However, to…
To overcome computational challenges of Optimal Transport (OT), several variants of Sliced Wasserstein (SW) has been developed in the literature. These approaches exploit the closed-form expression of the univariate OT by projecting…
While statistical modeling of distributional data has gained increased attention, the case of multivariate distributions has been somewhat neglected despite its relevance in various applications. This is because the Wasserstein distance,…
Wasserstein distance (WD) and the associated optimal transport plan have been proven useful in many applications where probability measures are at stake. In this paper, we propose a new proxy of the squared WD, coined min-SWGG, that is…
The sliced Wasserstein distance (SW) reduces optimal transport on $\mathbb{R}^d$ to a sum of one-dimensional projections, and thanks to this efficiency, it is widely used in geometry, generative modeling, and registration tasks. Recent work…
We introduce a distortion measure for images, Wasserstein distortion, that simultaneously generalizes pixel-level fidelity on the one hand and realism or perceptual quality on the other. We show how Wasserstein distortion reduces to a pure…
Approximate Bayesian Computation (ABC) is a popular method for approximate inference in generative models with intractable but easy-to-sample likelihood. It constructs an approximate posterior distribution by finding parameters for which…
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.…
In this paper, we consider the problem of computing the integral of a function on the unit sphere, in any dimension, using Monte Carlo methods. Although the methods we present are general, our guiding thread is the sliced Wasserstein…
The Wasserstein distance has been an attractive tool in many fields. But due to its high computational complexity and the phenomenon of the curse of dimensionality in empirical estimation, various extensions of the Wasserstein distance have…
We address the problem of computing a textural loss based on the statistics extracted from the feature activations of a convolutional neural network optimized for object recognition (e.g. VGG-19). The underlying mathematical problem is the…
Recently used in various machine learning contexts, the Gromov-Wasserstein distance (GW) allows for comparing distributions whose supports do not necessarily lie in the same metric space. However, this Optimal Transport (OT) distance…