Related papers: Wasserstein gradient flow for optimal probability …

We consider the population Wasserstein barycenter problem for random probability measures supported on a finite set of points and generated by an online stream of data. This leads to a complicated stochastic optimization problem where the…

This paper is concerned by statistical inference problems from a data set whose elements may be modeled as random probability measures such as multiple histograms or point clouds. We propose to review recent contributions in statistics on…

Robust optimization is a tractable and expressive technique for decision-making under uncertainty, but it can lead to overly conservative decisions when pessimistic assumptions are made on the uncertain parameters. Wasserstein…

One of the most popular approaches for solving total variation-regularized optimization problems in the space of measures are Particle Gradient Flows (PGFs). These restrict the problem to linear combinations of Dirac deltas and then perform…

Bayesian optimal experimental design (BOED) provides a powerful, decision-theoretic framework for selecting experiments so as to maximise the expected utility of the data to be collected. In practice, however, its applicability can be…

We investigate an expected utility maximization problem under model uncertainty in a one-period financial market. We capture model uncertainty by replacing the baseline model $\mathbb{P}$ with an adverse choice from a Wasserstein ball of…

We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed to bypass the computational intractability of exact optimal…

We consider approximating distributions within the framework of optimal mass transport and specialize to the problem of clustering data sets. Distances between distributions are measured in the Wasserstein metric. The main problem we…

We analyze the effect of small changes in the underlying probabilistic model on the value of multi-period stochastic optimization problems and optimal stopping problems. We work in finite discrete time and measure these changes with the…

Clustering is one of the most fundamental tools in data science and machine learning, and k-means clustering is one of the most common such methods. There is a variety of approximate algorithms for the k-means problem, but computing the…

We study the discretization of generalized Wasserstein distances with nonlinear mobilities on the real line via suitable discrete metrics on the cone of N ordered particles, a setting which naturally appears in the framework of…

We consider statistical methods which invoke a min-max distributionally robust formulation to extract good out-of-sample performance in data-driven optimization and learning problems. Acknowledging the distributional uncertainty in learning…

With the ongoing investment in data collection and communication technology in power systems, data-driven optimization has been established as a powerful tool for system operators to handle stochastic system states caused by weather- and…

This paper focuses on the contextual optimization problem where a decision is subject to some uncertain parameters and covariates that have some predictive power on those parameters are available before the decision is made. More…

Model Updating is frequently used in Structural Health Monitoring to determine structures' operating conditions and whether maintenance is required. Data collected by sensors are used to update the values of some initially unknown…

Many data clustering applications must handle objects that cannot be represented as vectors. In this context, the bag-of-vectors representation describes complex objects through discrete distributions, for which the Wasserstein distance…

The acceleration of gradient-based optimization methods is a subject of significant practical and theoretical importance, particularly within machine learning applications. While much attention has been directed towards optimizing within…

We propose a new clustering method based on optimal transportation. We solve optimal transportation with variational principles, and investigate the use of power diagrams as transportation plans for aggregating arbitrary domains into a…

We present and study a novel algorithm for the computation of 2-Wasserstein population barycenters of absolutely continuous probability measures on Euclidean space. The proposed method can be seen as a stochastic gradient descent procedure…

Generative modeling typically concerns transporting a single source distribution to a target distribution via simple probability flows. However, in fields like computer graphics and single-cell genomics, samples themselves can be viewed as…