Related papers: Recent Advances in Optimal Transport for Machine L…
Optimal mass transport is described by an approximation of transport cost via semi-discrete costs. The notions of optimal partition and optimal strong partition are given as well. We also suggest an algorithm for computation of Optimal…
This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport. While classical optimal transport considers only normalized probability distributions, it is important for…
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…
Machine learning assumes a pivotal role in our data-driven world. The increasing scale of models and datasets necessitates quick and reliable algorithms for model training. This dissertation investigates adaptivity in machine learning…
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…
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…
In machine learning, Optimal Transport (OT) theory is extensively utilized to compare probability distributions across various applications, such as graph data represented by node distributions and image data represented by pixel…
This letter investigates dynamical optimal transport of underactuated linear systems over an infinite time horizon. In our previous work, we proposed to integrate model predictive control and the celebrated Sinkhorn algorithm to perform…
We investigate the problem of sampling from posterior distributions with intractable normalizing constants in Bayesian inference. Our solution is a new generative modeling approach based on optimal transport (OT) that learns a deterministic…
Performative learning addresses the increasingly pervasive situations in which algorithmic decisions may induce changes in the data distribution as a consequence of their public deployment. We propose a novel view in which these…
Rectified flow (Liu et al., 2022; Liu, 2022; Wu et al., 2023) is a method for defining a transport map between two distributions, and enjoys popularity in machine learning, although theoretical results supporting the validity of these…
Machine learning develops rapidly, which has made many theoretical breakthroughs and is widely applied in various fields. Optimization, as an important part of machine learning, has attracted much attention of researchers. With the…
Transfer Optimization has gained a remarkable attention from the Swarm and Evolutionary Computation community in the recent years. It is undeniable that the concepts underlying Transfer Optimization are formulated on solid grounds. However,…
Optimal transportation theory is an area of mathematics with real-world applications in fields ranging from economics to optimal control to machine learning. We propose a new algorithm for solving discrete transport (network flow) problems,…
In the field of optimal transport, two prominent subfields face each other: (i) unregularized optimal transport, "\`a-la-Kantorovich", which leads to extremely sparse plans but with algorithms that scale poorly, and (ii)…
Sampling from diffusion probabilistic models (DPMs) can be viewed as a piecewise distribution transformation, which generally requires hundreds or thousands of steps of the inverse diffusion trajectory to get a high-quality image. Recent…
The traffic assignment problem (TAP) aims to predict how traffic flows distribute themselves across a road network, traditionally requiring computationally expensive iterative simulations to reach a user equilibrium (UE) where no driver can…
The task of learning to pick a single preferred example out a finite set of examples, an "optimal choice problem", is a supervised machine learning problem with complex, structured input. Problems of optimal choice emerge often in various…
We introduce an optimal transport-based model for learning a metric tensor from cross-sectional samples of evolving probability measures on a common Riemannian manifold. We neurally parametrize the metric as a spatially-varying matrix field…
Existing multimodal tasks mostly target at the complete input modality setting, i.e., each modality is either complete or completely missing in both training and test sets. However, the randomly missing situations have still been…