相关论文: Scenario Tree Reduction via Wasserstein Barycenter…

The discrete distribution is often used to describe complex instances in machine learning, such as images, sequences, and documents. Traditionally, clustering of discrete distributions (D2C) has been approached using Wasserstein barycenter…

Wasserstein barycenters define averages of probability measures in a geometrically meaningful way. Their use is increasingly popular in applied fields, such as image, geometry or language processing. In these fields however, the probability…

The main goal of this paper is to describe a new pruning method for solving decision trees and game trees. The pruning method for decision trees suggests a slight variant of decision trees that we call scenario trees. In scenario trees, we…

Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…

Euclidean Steiner trees are relevant to model minimal networks in real-world applications ubiquitously. In this paper, we study the feasibility of a hierarchical approach embedded with bundling operations to compute multiple and mutually…

We study the decentralized distributed computation of discrete approximations for the regularized Wasserstein barycenter of a finite set of continuous probability measures distributedly stored over a network. We assume there is a network of…

This paper presents a computational framework for the concise encoding of an ensemble of persistence diagrams, in the form of weighted Wasserstein barycenters [100], [102] of a dictionary of atom diagrams. We introduce a multi-scale…

Wasserstein barycenters have become popular due to their ability to represent the average of probability measures in a geometrically meaningful way. In this paper, we present an algorithm to approximate the Wasserstein-2 barycenters of…

Wasserstein barycentres represent average distributions between multiple probability measures for the Wasserstein distance. The numerical computation of Wasserstein barycentres is notoriously challenging. A common approach is to use…

A method was developed for Bayesian inference of species phylogeny using the multi-species coalescent model. To improve the mixing properties of the Markov chain Monte Carlo (MCMC) algorithm that traverses the space of species trees, we…

Wasserstein barycenters correspond to optimal solutions of transportation problems for several marginals, and as such have a wide range of applications ranging from economics to statistics and computer science. When the marginal probability…

Multi-stage decision-making under uncertainty, where decisions are taken under sequentially revealing uncertain problem parameters, is often essential to faithfully model managerial problems. Given the significant computational challenges…

In networks, there are often more than one source of capacity. The capacities can be permanently or temporarily owned by the decision maker. Depending on the nature of sources, we identify the permanent capacity, spot market capacity and…

The Wasserstein distance is a discrepancy measure between probability distributions, defined by an optimal transport problem. It has been used for various tasks such as retrieving similar items in high-dimensional images or text data. In…

We provide theoretical complexity analysis for new algorithms to compute the optimal transport (OT) distance between two discrete probability distributions, and demonstrate their favorable practical performance over state-of-art primal-dual…

Computing Wasserstein barycenters (a.k.a. Optimal Transport barycenters) is a fundamental problem in geometry which has recently attracted considerable attention due to many applications in data science. While there exist polynomial-time…

Efficiently computing the optimal control policy concerning a complicated future with stochastic disturbance has always been a challenge. The predicted stochastic future disturbance can be represented by a scenario tree, but solving the…

We investigate a simple approximation scheme, based on overlapping linear decision rules, for solving data-driven two-stage distributionally robust optimization problems with the type-$\infty$ Wasserstein ambiguity set. Our main result…

We study multistage distributionally robust linear optimization, where the uncertainty set is defined as a ball of distribution centered at a scenario tree using the nested distance. The resulting minimax problem is notoriously difficult to…

We develop an estimator-based stochastic fixed-point framework for approximately computing the 2-Wasserstein barycenter of continuous, non-parametric probability measures. Notably, we provide the first rigorous convergence analysis for…