相关论文: Safe Screening for Unbalanced Optimal Transport
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…
We consider a Beckmann formulation of an unbalanced optimal transport (UOT) problem. The $\Gamma$-convergence of this formulation of UOT to the corresponding optimal transport (OT) problem is established as the balancing parameter $\alpha$…
This paper studies online convex optimization with unknown linear budget constraints, where only the gradient information of the objective and the bandit feedback of constraint functions are observed. We propose a safe and efficient…
Unmanned Aerial Systems (UAS) have gained significant traction for their application in infrastructure inspections. However, considering the enormous scale and complex nature of infrastructure, automation is essential for improving the…
We consider the projected gradient algorithm for the nonconvex best subset selection problem that minimizes a given empirical loss function under an $\ell_0$-norm constraint. Through decomposing the feasible set of the given sparsity…
This paper addresses the problem of safe optimization under a single smooth constraint, a scenario that arises in diverse real-world applications such as robotics and autonomous navigation. The objective of safe optimization is to solve a…
Inverse optimal transport (OT) refers to the problem of learning the cost function for OT from observed transport plan or its samples. In this paper, we derive an unconstrained convex optimization formulation of the inverse OT problem,…
Stereo vision between images faces a range of challenges, including occlusions, motion, and camera distortions, across applications in autonomous driving, robotics, and face analysis. Due to parameter sensitivity, further complications…
Recently dictionary screening has been proposed as an effective way to improve the computational efficiency of solving the lasso problem, which is one of the most commonly used method for learning sparse representations. To address today's…
Group Ordered Weighted $L_{1}$-Norm (Group OWL) regularized models have emerged as a useful procedure for high-dimensional sparse multi-task learning with correlated features. Proximal gradient methods are used as standard approaches to…
Optimal Transport (OT) naturally arises in many machine learning applications, yet the heavy computational burden limits its wide-spread uses. To address the scalability issue, we propose an implicit generative learning-based framework…
We study the fundamental computational problem of approximating optimal transport (OT) equations using neural differential equations (Neural ODEs). More specifically, we develop a novel framework for approximating unbalanced optimal…
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…
Global pooling is one of the most significant operations in many machine learning models and tasks, whose implementation, however, is often empirical in practice. In this study, we develop a novel and solid global pooling framework through…
Non-negative and bounded-variable linear regression problems arise in a variety of applications in machine learning and signal processing. In this paper, we propose a technique to accelerate existing solvers for these problems by…
In logistic regression, it is often desirable to utilize regularization to promote sparse solutions, particularly for problems with a large number of features compared to available labels. In this paper, we present screening rules that…
Recently, linear regression models incorporating an optimal transport (OT) loss have been explored for applications such as supervised unmixing of spectra, music transcription, and mass spectrometry. However, these task-specific approaches…
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…
Consider a robot operating in an uncertain environment with stochastic, dynamic obstacles. Despite the clear benefits for trajectory optimization, it is often hard to keep track of each obstacle at every time step due to sensing and…
Bi-causal optimal transport (OT) is a natural framework for comparing and coupling stochastic processes under nonanticipative information constraints, with important applications in robust finance, sequential uncertainty quantification, and…