相关论文: LCOT: Linear circular optimal transport

Semi-discrete optimal transport (SOT), which maps a continuous probability measure to a discrete one, is a fundamental problem with wide-ranging applications. Entropic regularization is often employed to solve the SOT problem, leading to a…

In this paper, we address the numerical solution to the multimarginal optimal transport (MMOT) with pairwise costs. MMOT, as a natural extension from the classical two-marginal optimal transport, has many important applications including…

The Skorokhod embedding problem is to represent a given probability as the distribution of Brownian motion at a chosen stopping time. Over the last 50 years this has become one of the important classical problems in probability theory and a…

In this paper, a novel circular and structural operator tracker (CSOT) is proposed for high performance visual tracking, it not only possesses the powerful discriminative capability of SOSVM but also efficiently inherits the superior…

We investigate the use of entropy-regularized optimal transport (EOT) cost in developing generative models to learn implicit distributions. Two generative models are proposed. One uses EOT cost directly in an one-shot optimization problem…

Metric learning seeks perceptual embeddings where visually similar instances are close and dissimilar instances are apart, but learned representations can be sub-optimal when the distribution of intra-class samples is diverse and distinct…

Optimal mass transport, also known as the earth mover's problem, is an optimization problem with important applications in various disciplines, including economics, probability theory, fluid dynamics, cosmology and geophysics to cite a few.…

Monge-Kantorovich optimal mass transport (OMT) provides a blueprint for geometries in the space of positive densities -- it quantifies the cost of transporting a mass distribution into another. In particular, it provides natural options for…

The optimal transport (OT) problem aims to find the most efficient mapping between two probability distributions under a given cost function, and has diverse applications in many fields such as machine learning, computer vision and computer…

Multi-task learning (MTL) has emerged as a pivotal paradigm in machine learning by leveraging shared structures across multiple related tasks. Despite its empirical success, the development of likelihood-based efficiently solvable…

This paper addresses the problem of estimating entropy-regularized optimal transport (EOT) maps with squared-Euclidean cost between source and target measures that are subGaussian. In the case that the target measure is compactly supported…

Optimal Transport (OT) distances are now routinely used as loss functions in ML tasks. Yet, computing OT distances between arbitrary (i.e. not necessarily discrete) probability distributions remains an open problem. This paper introduces a…

We introduce the Smoothed Online Optimization for Target Tracking (SOOTT) problem, a new framework that integrates three key objectives in online decision-making under uncertainty: (1) tracking cost for following a dynamically moving…

Most uncertainty quantification (UQ) approaches provide a single scalar value as a measure of model reliability. However, different uncertainty measures could provide complementary information on the prediction confidence. Even measures…

Given a learning problem with real-world tradeoffs, which cost function should the model be trained to optimize? This is the metric selection problem in machine learning. Despite its practical interest, there is limited formal guidance on…

Imitation learning algorithms have been interpreted as variants of divergence minimization problems. The ability to compare occupancy measures between experts and learners is crucial in their effectiveness in learning from demonstrations.…

Optimal transport (OT) is a versatile framework for comparing probability measures, with many applications to statistics, machine learning, and applied mathematics. However, OT distances suffer from computational and statistical scalability…

We propose the use of Flat Metric to assess the performance of reconstruction methods for single-molecule localization microscopy (SMLM) in scenarios where the ground-truth is available. Flat Metric is intimately related to the concept of…

Bearing measurements,as the most common modality in nature, have recently gained traction in multi-robot systems to enhance mutual localization and swarm collaboration. Despite their advantages, challenges such as sensory noise, obstacle…

Optimal transport (OT) and unbalanced optimal transport (UOT) are central in many machine learning, statistics and engineering applications. 1D OT is easily solved, with complexity O(n log n), but no efficient algorithm was known for 1D…