Related papers: Schema matching using Gaussian mixture models with…
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…
Gaussian mixture models (GMMs) are widely used in machine learning for tasks such as clustering, classification, image reconstruction, and generative modeling. A key challenge in working with GMMs is defining a computationally efficient and…
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…
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…
This paper uses sample data to study the problem of comparing populations on finite-dimensional parallelizable Riemannian manifolds and more general trivial vector bundles. Utilizing triviality, our framework represents populations as…
The Wasserstein distance between mixing measures has come to occupy a central place in the statistical analysis of mixture models. This work proposes a new canonical interpretation of this distance and provides tools to perform inference on…
Understanding proper distance measures between distributions is at the core of several learning tasks such as generative models, domain adaptation, clustering, etc. In this work, we focus on mixture distributions that arise naturally in…
Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive…
The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…
The Gromov-Wasserstein (GW) distance is frequently used in machine learning to compare distributions across distinct metric spaces. Despite its utility, it remains computationally intensive, especially for large-scale problems. Recently, a…
Generalized Wasserstein distances allow to quantitatively compare two continuous or atomic mass distributions with equal or different total mass. In this paper, we propose four numerical methods for the approximation of three different…
Gaussian Mixture Models are a powerful tool in Data Science and Statistics that are mainly used for clustering and density approximation. The task of estimating the model parameters is in practice often solved by the Expectation…
In this work we study systems consisting of a group of moving particles. In such systems, often some important parameters are unknown and have to be estimated from observed data. Such parameter estimation problems can often be solved via a…
Gaussian mixture models (GMM) are powerful parametric tools with many applications in machine learning and computer vision. Expectation maximization (EM) is the most popular algorithm for estimating the GMM parameters. However, EM…
In this article, we study Wasserstein-type metrics and corresponding barycenters for mixtures of a chosen subset of probability measures called atoms hereafter. In particular, this works extends what was proposed by Delon and Desolneux [A…
The clustering algorithms that view each object data as a single sample drawn from a certain distribution, Gaussian distribution, for example, has been a hot topic for decades. Many clustering algorithms: such as k-means and spectral…
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…
We address the problem of efficiently computing Wasserstein distances for multiple pairs of distributions drawn from a meta-distribution. To this end, we propose a fast estimation method based on regressing Wasserstein distance on sliced…
Comparing images to recommend items from an image-inventory is a subject of continued interest. Added with the scalability of deep-learning architectures the once `manual' job of hand-crafting features have been largely alleviated, and…
Using statistical learning methods to analyze stochastic simulation outputs can significantly enhance decision-making by uncovering relationships between different simulated systems and between a system's inputs and outputs. We focus on…