相关论文: Wasserstein total variation filtering

The Wasserstein barycenter extends the Euclidean mean to the space of probability measures by minimizing the weighted sum of squared 2-Wasserstein distances. We develop a free-support algorithm for computing Wasserstein barycenters that…

In this study, we introduce novel methodologies designed to adapt original data in response to the dynamics of persistence diagrams along Wasserstein gradient flows. Our research focuses on the development of algorithms that translate…

The Boltzmann machine provides a useful framework to learn highly complex, multimodal and multiscale data distributions that occur in the real world. The default method to learn its parameters consists of minimizing the Kullback-Leibler…

We consider the Wasserstein metric on the Gaussian mixture models (GMMs), which is defined as the pullback of the full Wasserstein metric on the space of smooth probability distributions with finite second moment. It derives a class of…

Wasserstein distance is a key metric for quantifying data divergence from a distributional perspective. However, its application in privacy-sensitive environments, where direct sharing of raw data is prohibited, presents significant…

Profiling cellular phenotypes from microscopic imaging can provide meaningful biological information resulting from various factors affecting the cells. One motivating application is drug development: morphological cell features can be…

We study the problem of distributional matrix completion: Given a sparsely observed matrix of empirical distributions, we seek to impute the true distributions associated with both observed and unobserved matrix entries. This is a…

With the rapid development of online payment platforms, it is now possible to record massive transaction data. Clustering on transaction data significantly contributes to analyzing merchants' behavior patterns. This enables payment…

Persistence diagrams are a useful tool from topological data analysis which can be used to provide a concise description of a filtered topological space. What makes them even more useful in practice is that they come with a notion of a…

The subject of this paper is the estimation of a probability measure on ${\mathbb R}^d$ from data observed with an additive noise, under the Wasserstein metric of order $p$ (with $p\geq 1$). We assume that the distribution of the errors is…

We propose a novel framework for learning time-varying graphs from spatiotemporal measurements. Given an appropriate prior on the temporal behavior of signals, our proposed method can estimate time-varying graphs from a small number of…

The validation of global climate models is crucial to ensure the accuracy and efficacy of model output. We introduce the spherical convolutional Wasserstein distance to more comprehensively measure differences between climate models and…

Adversarial examples are crafted by adding indistinguishable perturbations to normal examples in order to fool a well-trained deep learning model to misclassify. In the context of computer vision, this notion of indistinguishability is…

In this work, we analyze the properties of the solution to the covariance steering problem for discrete time Gaussian linear systems with a squared Wasserstein distance terminal cost. In our previous work, we have shown that by utilizing…

We consider probabilistic models for sequential observations which exhibit gradual transitions among a finite number of states. We are particularly motivated by applications such as human activity analysis where observed accelerometer time…

Wasserstein barycenters provide a geometric notion of the weighted average of probability measures based on optimal transport. In this paper, we present a scalable algorithm to compute Wasserstein-2 barycenters given sample access to the…

Many data clustering applications must handle objects that cannot be represented as vectors. In this context, the bag-of-vectors representation describes complex objects through discrete distributions, for which the Wasserstein distance…

This paper addresses the problem of segmenting a time-series with respect to changes in the mean value or in the variance. The first case is when the time data is modeled as a sequence of independent and normal distributed random variables…

This paper deals with the estimation of a probability measure on the real line from data observed with an additive noise. We are interested in rates of convergence for the Wasserstein metric of order $p\geq 1$. The distribution of the…

Squared Wasserstein distance is a frequently used tool to measure discrepancy between probability distributions. This distance is typically computed between empirical measures of size $n$ from two underlying random samples. Unfortunately,…