Related papers: A fast algorithm for Earth Mover's Distance based …
We propose an adaptive finite element algorithm to approximate solutions of elliptic problems whose forcing data is locally defined and is approximated by regularization (or mollification). We show that the energy error decay is…
Optimal transportation distances are a fundamental family of parameterized distances for histograms. Despite their appealing theoretical properties, excellent performance in retrieval tasks and intuitive formulation, their computation…
In the geometric transportation problem, we are given a collection of points $P$ in $d$-dimensional Euclidean space, and each point is given a supply of $\mu(p)$ units of mass, where $\mu(p)$ could be a positive or a negative integer, and…
We study the problem of minimizing a sum of local objective convex functions over a network of processors/agents. This problem naturally calls for distributed optimization algorithms, in which the agents cooperatively solve the problem…
A regularized minimization model with $l_1$-norm penalty (RP) is introduced for training the autoencoders that belong to a class of two-layer neural networks. We show that the RP can act as an exact penalty model which shares the same…
We study the proximal gradient descent (PGD) method for $\ell^{0}$ sparse approximation problem as well as its accelerated optimization with randomized algorithms in this paper. We first offer theoretical analysis of PGD showing the bounded…
This paper investigates the semi-discrete optimal transport (OT) problem with entropic regularization. We characterize the solution using a governing, well-posed ordinary differential equation (ODE). This naturally yields an algorithm to…
The modeling of phenomenological structure is a crucial aspect in inverse imaging problems. One emerging modeling tool in computational imaging is the optimal transport framework. Its ability to model geometric displacements across an…
This paper presents a novel extended dynamic programming approach for energy minimization (EDP) to solve the correspondence problem for stereo and motion. A significant speedup is achieved using a recursive minimum search strategy (RMS).…
This paper aims to develop new and fast algorithms for recovering a sparse vector from a small number of measurements, which is a fundamental problem in the field of compressive sensing (CS). Currently, CS favors incoherent systems, in…
Optimal transport (OT) serves as a natural framework for comparing probability measures, with applications in statistics, machine learning, and applied mathematics. Alas, statistical estimation and exact computation of the OT distances…
We study the optimal transport problem for $d>2$ discrete measures. This is a linear programming problem on $d$-tensors. It gives a way to compute a "distance" between two sets of discrete measures. We introduce an entropic regularization…
Incorporating a non-Euclidean variable metric to first-order algorithms is known to bring enhancement. However, due to the lack of an optimal choice, such an enhancement appears significantly underestimated. In this work, we establish a…
We study the unbalanced optimal transport (UOT) problem, where the marginal constraints are enforced using Maximum Mean Discrepancy (MMD) regularization. Our work is motivated by the observation that the literature on UOT is focused on…
In this study, we propose an algorithmic framework for solving a class of optimal control problems. This class is associated with the minimum-time interception of moving target problems, where a plant with a given state equation must…
Recent advances in multimodal learning have largely relied on pairwise contrastive objectives to align different modalities, such as text, video, and audio, in a shared embedding space. While effective in bi-modal setups, these approaches…
Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…
We propose a new method for computing Dynamic Mode Decomposition (DMD) evolution matrices, which we use to analyze dynamical systems. Unlike the majority of existing methods, our approach is based on a variational formulation consisting of…
In the regime of bounded transportation costs, additive approximations for the optimal transport problem are reduced (rather simply) to relative approximations for positive linear programs, resulting in faster additive approximation…
The earth mover's distance (EMD), also known as the 1-Wasserstein metric, measures the minimum amount of work required to transform one probability distribution into another. The EMD can be naturally generalized to measure the "distance"…