Related papers: Schema matching using Gaussian mixture models with…
Sliced Wasserstein distances are widely used in practice as a computationally efficient alternative to Wasserstein distances in high dimensions. In this paper, motivated by theoretical foundations of this alternative, we prove quantitative…
Computing the infinity Wasserstein distance and retrieving projections of a probability measure onto a closed subset of probability measures are critical sub-problems in various applied fields. However, the practical applicability of these…
We give an efficient algorithm for robustly clustering of a mixture of two arbitrary Gaussians, a central open problem in the theory of computationally efficient robust estimation, assuming only that the the means of the component Gaussians…
Mixture models are widely used in Bayesian statistics and machine learning, in particular in computational biology, natural language processing and many other fields. Variational inference, a technique for approximating intractable…
Recently, enthusiastic studies have devoted to texture synthesis using deep neural networks, because these networks excel at handling complex patterns in images. In these models, second-order statistics, such as Gram matrix, are used to…
In this paper, we establish sharp upper and lower bounds on the convergence rate of the empirical measures of point processes under the Wasserstein distance. To this end, we first introduce a new metric on the space of counting measures…
Clustering is a widely used technique with a long and rich history in a variety of areas. However, most existing algorithms do not scale well to large datasets, or are missing theoretical guarantees of convergence. This paper introduces a…
The paper introduces a methodology for visualizing on a dimension reduced subspace the classification structure and the geometric characteristics induced by an estimated Gaussian mixture model for discriminant analysis. In particular, we…
The Sliced-Wasserstein distance (SW) is being increasingly used in machine learning applications as an alternative to the Wasserstein distance and offers significant computational and statistical benefits. Since it is defined as an…
Wasserstein Discriminant Analysis (WDA) is a new supervised method that can improve classification of high-dimensional data by computing a suitable linear map onto a lower dimensional subspace. Following the blueprint of classical Linear…
In the study of dynamical and physical systems, the input parameters are often uncertain or randomly distributed according to a measure $\varrho$. The system's response $f$ pushes forward $\varrho$ to a new measure $f\circ \varrho$ which we…
Finite mixture models are a useful statistical model class for clustering and density approximation. In the Bayesian framework finite mixture models require the specification of suitable priors in addition to the data model. These priors…
The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the {\it correct target clustering} of the samples…
This paper presents a new distance metric to compare two continuous probability density functions. The main advantage of this metric is that, unlike other statistical measurements, it can provide an analytic, closed-form expression for a…
The classical Gaussian mixture model assumes homogeneity within clusters, an assumption that often fails in real-world data where observations naturally exhibit varying scales or intensities. To address this, we introduce the…
Flow matching has recently emerged as a flexible and efficient framework for generative modelling by learning deterministic transport dynamics between probability measures. In this work, we extend flow matching to the space of probability…
The Wasserstein distance is a discrepancy measure between probability distributions, defined by an optimal transport problem. It has been used for various tasks such as retrieving similar items in high-dimensional images or text data. In…
Wasserstein distance, which measures the discrepancy between distributions, shows efficacy in various types of natural language processing (NLP) and computer vision (CV) applications. One of the challenges in estimating Wasserstein distance…
We consider the general dimensionality reduction problem of locating in a high-dimensional data cloud, a $k$-dimensional non-Gaussian subspace of interesting features. We use a projection pursuit approach -- we search for mutually…
In transportation network analysis, various types of road network data can be used even when focusing on the same region. Since different road network datasets can make different performance in analyses, it is necessary to compare them and…