Related papers: Minimum Wasserstein Distance Estimator under Finit…
We present the first minimax risk bounds for estimators of the spectral measure in multivariate linear factor models, where observations are linear combinations of regularly varying latent factors. Non-asymptotic convergence rates are…
Optimal transport distances are powerful tools to compare probability distributions and have found many applications in machine learning. Yet their algorithmic complexity prevents their direct use on large scale datasets. To overcome this…
The likelihood function of a finite mixture model is a non-convex function with multiple local maxima and commonly used iterative algorithms such as EM will converge to different solutions depending on initial conditions. In this paper we…
In this paper, different strands of literature are combined in order to obtain algorithms for semi-parametric estimation of discrete choice models that include the modelling of unobserved heterogeneity by using mixing distributions for the…
Motivated by the growing popularity of variants of the Wasserstein distance in statistics and machine learning, we study statistical inference for the Sliced Wasserstein distance--an easily computable variant of the Wasserstein distance.…
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…
Learning conditional densities and identifying factors that influence the entire distribution are vital tasks in data-driven applications. Conventional approaches work mostly with summary statistics, and are hence inadequate for a…
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…
Wasserstein distances are increasingly used in a wide variety of applications in machine learning. Sliced Wasserstein distances form an important subclass which may be estimated efficiently through one-dimensional sorting operations. In…
We propose a new statistical model, the spiked transport model, which formalizes the assumption that two probability distributions differ only on a low-dimensional subspace. We study the minimax rate of estimation for the Wasserstein…
Optimal transport distances, otherwise known as Wasserstein distances, have recently drawn ample attention in computer vision and machine learning as a powerful discrepancy measure for probability distributions. The recent developments on…
This paper considers the fusion of multiple estimates of a spatially extended object, where the object extent is modeled as an ellipse parameterized by the orientation and semiaxes lengths. For this purpose, we propose a novel systematic…
Introduced by Kiefer and Wolfowitz \cite{KW56}, the nonparametric maximum likelihood estimator (NPMLE) is a widely used methodology for learning mixture odels and empirical Bayes estimation. Sidestepping the non-convexity in mixture…
This paper studies the optimal rate of estimation in a finite Gaussian location mixture model in high dimensions without separation conditions. We assume that the number of components $k$ is bounded and that the centers lie in a ball of…
We study the maximum likelihood estimation (MLE) in the multivariate deviated model where the data are generated from the density function $(1-\lambda^{\ast})h_{0}(x)+\lambda^{\ast}f(x|\mu^{\ast}, \Sigma^{\ast})$ in which $h_{0}$ is a known…
Word embeddings are high dimensional vector representations of words that capture their semantic similarity in the vector space. There exist several algorithms for learning such embeddings both for a single language as well as for several…
Wasserstein distributionally robust optimization estimators are obtained as solutions of min-max problems in which the statistician selects a parameter minimizing the worst-case loss among all probability models within a certain distance…
We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our…
Optimal Transport (OT) metrics allow for defining discrepancies between two probability measures. Wasserstein distance is for longer the celebrated OT-distance frequently-used in the literature, which seeks probability distributions to be…
Statistical inference can be performed by minimizing, over the parameter space, the Wasserstein distance between model distributions and the empirical distribution of the data. We study asymptotic properties of such minimum Wasserstein…