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Distributionally-robust optimization is often studied for a fixed set of distributions rather than time-varying distributions that can drift significantly over time (which is, for instance, the case in finance and sociology due to…

The sliced Wasserstein distance as well as its variants have been widely considered in comparing probability measures defined on $\mathbb R^d$. Here we derive the notion of sliced Wasserstein distance for measures on an infinite dimensional…

In the field of modern high-energy physics research, there is a growing emphasis on utilizing deep learning techniques to optimize event simulation, thereby expanding the statistical sample size for more accurate physical analysis.…

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…

We study estimation problems in safety-critical applications with streaming data. Since estimation problems can be posed as optimization problems in the probability space, we devise a stochastic projected Wasserstein gradient flow that…

In this manuscript we investigate the equivalence of Fourier-based metrics on discrete state spaces with the well-known Wasserstein distances. While the use of Fourier-based metrics in continuous state spaces is ubiquitous since its…

Persistence diagrams (PD)s play a central role in topological data analysis, and are used in an ever increasing variety of applications. The comparison of PD data requires computing comparison metrics among large sets of PDs, with metrics…

Statistical solutions have recently been introduced as a an alternative solution framework for hyperbolic systems of conservation laws. In this work we derive a novel a posteriori error estimate in the Wasserstein distance between…

The empirical Wasserstein projection (WP) distance quantifies the Wasserstein distance from the empirical distribution to a set of probability measures satisfying given expectation constraints. The WP is a powerful tool because it mitigates…

The theory of optimal transport of probability measures has wide-ranging applications across a number of different fields, including concentration of measure, machine learning, Markov chains, and economics. The generalisation of optimal…

We present a methodology for predictable and safe covariance steering control of uncertain nonlinear stochastic processes. The systems under consideration are subject to general uncertainties, which include unbounded random disturbances…

In this work we investigate gradient estimation for a class of contracting stochastic systems on a continuous state space. We find conditions on the one-step transitions, namely differentiability and contraction in a Wasserstein distance,…

This paper targets the task with discrete and periodic class labels ($e.g.,$ pose/orientation estimation) in the context of deep learning. The commonly used cross-entropy or regression loss is not well matched to this problem as they ignore…

Wasserstein geometry and information geometry are two important structures to be introduced in a manifold of probability distributions. Wasserstein geometry is defined by using the transportation cost between two distributions, so it…

We propose a distributionally robust data-driven predictive control framework for stochastic linear time-invariant systems with unknown dynamics and disturbance distributions. We use an offline trajectory to fit the subspace predictive…

Wasserstein dictionary learning is an unsupervised approach to learning a collection of probability distributions that generate observed distributions as Wasserstein barycentric combinations. Existing methods for Wasserstein dictionary…

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…

Determinantal point processes (DPPs) have received significant attention as an elegant probabilistic model for discrete subset selection. Most prior work on DPP learning focuses on maximum likelihood estimation (MLE). While efficient and…

In this paper, we provide sufficient conditions for the existence of the invariant distribution and for subgeometric rates of convergence in Wasserstein distance for general state-space Markov chains which are (possibly) not irreducible.…

A probabilistic framework to study the dependence structure induced by deterministic discrete-time state-space systems between input and output processes is introduced. General sufficient conditions are formulated under which output…