Related papers: Unbalanced Optimal Transport through Non-negative …
We propose a novel approach based on optimal transport (OT) for tackling the problem of highly mixed data in blind hyperspectral unmixing. Our method constrains the distribution of the estimated abundance matrix to resemble a targeted…
In several applications, including imaging of deformable objects while in motion, simultaneous localization and mapping, and unlabeled sensing, we encounter the problem of recovering a signal that is measured subject to unknown…
Unbalanced optimal transport (UOT) provides a flexible way to match or compare nonnegative finite Radon measures. However, UOT requires a predefined ground transport cost, which may misrepresent the data's underlying geometry. Choosing such…
In this paper we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints, are locally smooth. For solving this problem, we propose a…
Neural network-based optimal transport (OT) is a recent and fruitful direction in the generative modeling community. It finds its applications in various fields such as domain translation, image super-resolution, computational biology and…
The objective of this paper is to develop a duality between a novel Entropy Martingale Optimal Transport problem (A) and an associated optimization problem (B). In (A) we follow the approach taken in the Entropy Optimal Transport (EOT)…
Recovering nonlinearly degraded signal in the presence of noise is a challenging problem. In this work, this problem is tackled by minimizing the sum of a non convex least-squares fit criterion and a penalty term. We assume that the…
In this paper, we introduce a generalized dynamical unbalanced optimal transport framework by incorporating limited control input and mass dissipation, addressing limitations in conventional optimal transport for control applications. We…
Optimal transport distances have found many applications in machine learning for their capacity to compare non-parametric probability distributions. Yet their algorithmic complexity generally prevents their direct use on large scale…
We consider the problem of incentivization and optimal control of autonomous vehicles for improving traffic congestion. In our scenario, autonomous vehicles must be incentivized in order to participate in traffic improvement. Using the…
This paper introduces a graph-based algorithm for solving single-item, single-location inventory lot-sizing problems under non-stationary stochastic demand using the $(R_t, S_t)$ policy and a penalty cost scheme. The proposed method relaxes…
While the optimal transport (OT) problem was originally formulated as a linear program, the addition of entropic regularization has proven beneficial both computationally and statistically, for many applications. The Sinkhorn fixed-point…
The nonlinear filtering problem is concerned with finding the conditional probability distribution (posterior) of the state of a stochastic dynamical system, given a history of partial and noisy observations. This paper presents a…
We present a general convex relaxation approach to study a wide class of Unbalanced Optimal Transport problems for finite non-negative measures with possibly different masses. These are obtained as the lower semicontinuous and convex…
We propose a novel exact algorithm for the transportation problem, one of the paradigmatic network optimization problems. The algorithm, denoted Iterated Inside Out, requires in input a basic feasible solution and is composed by two main…
Optimization is a ubiquitous modeling tool and is often deployed in settings which repeatedly solve similar instances of the same problem. Amortized optimization methods use learning to predict the solutions to problems in these settings,…
Optimal transport (OT) finds a least cost transport plan between two probability distributions using a cost matrix defined on pairs of points. Unlike standard OT, which infers unstructured pointwise mappings, low-rank optimal transport…
Optimal Transport (OT) is a resource allocation problem with applications in biology, data science, economics and statistics, among others. In some of the applications, practitioners have access to samples which approximate the continuous…
Optimal Transport (OT) has fueled machine learning (ML) across many domains. When paired data measurements $(\boldsymbol{\mu}, \boldsymbol{\nu})$ are coupled to covariates, a challenging conditional distribution learning setting arises.…
We propose a protocol optimization technique that is applicable to both weighted or unweighted graphs. Our aim is to explore by how much a small variation around the Shortest Path or Optimal Path protocols can enhance protocol performance.…