Related papers: Wasserstein statistics in 1D location-scale model
In this paper, we introduce a generalization of the Wasserstein barycenter, to a case where the initial probability measures live on different subspaces of R^d. We study the existence and uniqueness of this barycenter, we show how it is…
We formulate and solve a regression problem with time-stamped distributional data. Distributions are considered as points in the Wasserstein space of probability measures, metrized by the 2-Wasserstein metric, and may represent images,…
Impractical assumptions, an inherently myopic nature, and the crucial role of the initial design, all together contribute to making theoretical convergence proofs of little value in real-life Bayesian Optimization applications. In this…
We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…
We study the interaction between entropy and Wasserstein distance in free probability theory. In particular, we give lower bounds for several versions of free entropy dimension along Wasserstein geodesics, as well as study their topological…
We provide non asymptotic rates of convergence of the Wasserstein Generative Adversarial networks (WGAN) estimator. We build neural networks classes representing the generators and discriminators which yield a GAN that achieves the minimax…
In the past couple of years, various approaches to representing and quantifying different types of predictive uncertainty in machine learning, notably in the setting of classification, have been proposed on the basis of second-order…
We study optimization problems whereby the optimization variable is a probability measure. Since the probability space is not a vector space, many classical and powerful methods for optimization (e.g., gradients) are of little help. Thus,…
Random fields are useful mathematical objects in the characterization of non-deterministic complex systems. A fundamental issue in the evolution of dynamical systems is how intrinsic properties of such structures change in time. In this…
Ranking distributions according to a stochastic order has wide applications in diverse areas. Although stochastic dominance has received much attention, convex order, particularly in general dimensions, has yet to be investigated from a…
Borel probability measures living on metric spaces are fundamental mathematical objects. There are several meaningful distance functions that make the collection of the probability measures living on a certain space a metric space. We are…
The sliced Wasserstein (SW) distance has been widely recognized as a statistically effective and computationally efficient metric between two probability measures. A key component of the SW distance is the slicing distribution. There are…
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…
As the demand to integrate Artificial Intelligence into high-stakes environments continues to grow, explaining the reasoning behind neural-network predictions has shifted from a theoretical curiosity to a strict operational requirement. Our…
We introduce a new information-geometric structure associated with the dynamics on discrete objects such as graphs and hypergraphs. The presented setup consists of two dually flat structures built on the vertex and edge spaces,…
Manifold hypothesis states that data points in high-dimensional space actually lie in close vicinity of a manifold of much lower dimension. In many cases this hypothesis was empirically verified and used to enhance unsupervised and…
Many applications in machine learning involve data represented as probability distributions. The emergence of such data requires radically novel techniques to design tractable gradient flows on probability distributions over this type of…
In this paper, we study statistical inference for the Wasserstein distance, which has attracted much attention and has been applied to various machine learning tasks. Several studies have been proposed in the literature, but almost all of…
Optimal transport provides an inherently geometric and highly structured framework for studying spaces of probability measures, supplying a rich theoretical toolkit for contemporary statistics, machine learning, and generative modelling. In…
Efficiently accessing the information contained in non-linear and high dimensional probability distributions remains a core challenge in modern statistics. Traditionally, estimators that go beyond point estimates are either categorized as…