Related papers: Wasserstein-based Kernel Principal Component Analy…

This paper presents a computational framework for the concise encoding of an ensemble of persistence diagrams, in the form of weighted Wasserstein barycenters [100], [102] of a dictionary of atom diagrams. We introduce a multi-scale…

Modeling observations as random distributions embedded within Wasserstein spaces is becoming increasingly popular across scientific fields, as it captures the variability and geometric structure of the data more effectively. However, the…

Recently, a Wasserstein-type distance for Gaussian mixture models has been proposed. However, that framework can only be generalized to identifiable mixtures of general elliptically contoured distributions whose components come from the…

Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…

Measuring the distance between ontological elements is fundamental for ontology matching. String-based distance metrics are notorious for shallow syntactic matching. In this exploratory study, we investigate Wasserstein distance targeting…

We introduce a novel, geometry-aware distance metric for the family of von Mises-Fisher (vMF) distributions, which are fundamental models for directional data on the unit hypersphere. Although the vMF distribution is widely employed in a…

In this work we analyse a number of variants of the Wasserstein distance which allow to focus the classification on the prescribed parts (fragments) of classified 2D curves. These variants are based on the use of a number of discrete…

We present new algorithms to compute the mean of a set of empirical probability measures under the optimal transport metric. This mean, known as the Wasserstein barycenter, is the measure that minimizes the sum of its Wasserstein distances…

Existing approaches to depth or disparity estimation output a distribution over a set of pre-defined discrete values. This leads to inaccurate results when the true depth or disparity does not match any of these values. The fact that this…

A novel framework for density estimation under expectation constraints is proposed. The framework minimizes the Wasserstein distance between the estimated density and a prior, subject to the constraints that the expected value of a set of…

Stacking Gaussian Processes severely diminishes the model's ability to detect outliers, which when combined with non-zero mean functions, further extrapolates low non-parametric variance to low training data density regions. We propose a…

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,…

Motivated by problems in data clustering, we establish general conditions under which families of nonparametric mixture models are identifiable, by introducing a novel framework involving clustering overfitted \emph{parametric} (i.e.…

The squared Wasserstein distance is a natural quantity to compare probability distributions in a non-parametric setting. This quantity is usually estimated with the plug-in estimator, defined via a discrete optimal transport problem which…

This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…

Similarity-based clustering and semi-supervised learning methods separate the data into clusters or classes according to the pairwise similarity between the data, and the pairwise similarity is crucial for their performance. In this paper,…

We consider the problem of clustering functional data according to their covariance structure. We contribute a soft clustering methodology based on the Wasserstein-Procrustes distance, where the in-between cluster variability is penalised…

Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…

A novel variational inference based resampling framework is proposed to evaluate the robustness and generalization capability of deep learning models with respect to distribution shift. We use Auto Encoding Variational Bayes to find a…

Robust optimization is a tractable and expressive technique for decision-making under uncertainty, but it can lead to overly conservative decisions when pessimistic assumptions are made on the uncertain parameters. Wasserstein…