Related papers: Wasserstein Exponential Kernels
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…
In this work we test Wasserstein distance in conjunction with persistent homology, as a tool for discriminating large scale structures of simulated universes with different values of $\sigma_8$ cosmological parameter (present…
In this work, we investigate Gaussian Processes indexed by multidimensional distributions. While directly constructing radial positive definite kernels based on the Wasserstein distance has been proven to be possible in the unidimensional…
Defining meaningful distances between samples in a dataset is a fundamental problem in machine learning. Optimal Transport (OT) lifts a distance between features (the "ground metric") to a geometrically meaningful distance between samples.…
This paper introduces Wasserstein variational inference, a new form of approximate Bayesian inference based on optimal transport theory. Wasserstein variational inference uses a new family of divergences that includes both f-divergences and…
Algebraic topology methods have recently played an important role for statistical analysis with complicated geometric structured data such as shapes, linked twist maps, and material data. Among them, \textit{persistent homology} is a…
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…
Distance metrics and their nonlinear variant play a crucial role in machine learning based real-world problem solving. We demonstrated how Euclidean and cosine distance measures differ not only theoretically but also in real-world medical…
It was recently shown that under smoothness conditions, the squared Wasserstein distance between two distributions could be efficiently computed with appealing statistical error upper bounds. However, rather than the distance itself, the…
We introduce Deep Set Linearized Optimal Transport, an algorithm designed for the efficient simultaneous embedding of point clouds into an $L^2-$space. This embedding preserves specific low-dimensional structures within the Wasserstein…
In this paper, we investigate the properties of the Sliced Wasserstein Distance (SW) when employed as an objective functional. The SW metric has gained significant interest in the optimal transport and machine learning literature, due to…
Bayesian inference problems require sampling or approximating high-dimensional probability distributions. The focus of this paper is on the recently introduced Stein variational gradient descent methodology, a class of algorithms that rely…
Predictive states for stochastic processes are a nonparametric and interpretable construct with relevance across a multitude of modeling paradigms. Recent progress on the self-supervised reconstruction of predictive states from time-series…
In this work clustering schemes for uncertain and structured data are considered relying on the notion of Wasserstein barycenters, accompanied by appropriate clustering indices based on the intrinsic geometry of the Wasserstein space where…
We propose a scalable robust learning algorithm combining kernel smoothing and robust optimization. Our method is motivated by the convex analysis perspective of distributionally robust optimization based on probability metrics, such as the…
Recent years have witnessed a tremendous growth using topological summaries, especially the persistence diagrams (encoding the so-called persistent homology) for analyzing complex shapes. Intuitively, persistent homology maps a potentially…
While theoretically appealing, the application of the Wasserstein distance to large-scale machine learning problems has been hampered by its prohibitive computational cost. The sliced Wasserstein distance and its variants improve the…
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 discuss the relation between the Wasserstein distance of order 1 between probability distributions on a metric space, arising in the study of Monge-Kantorovich transport problem, and the spectral distance of noncommutative geometry.…
Herding and kernel herding are deterministic methods of choosing samples which summarise a probability distribution. A related task is choosing samples for estimating integrals using Bayesian quadrature. We show that the criterion minimised…