Related papers: Learning to Match via Inverse Optimal Transport

This paper proposes a novel federated algorithm that leverages momentum-based variance reduction with adaptive learning to address non-convex settings across heterogeneous data. We intend to minimize communication and computation overhead,…

We propose a new method to estimate Wasserstein distances and optimal transport plans between two probability distributions from samples in high dimension. Unlike plug-in rules that simply replace the true distributions by their empirical…

Adversarial examples have pointed out Deep Neural Networks vulnerability to small local noise. It has been shown that constraining their Lipschitz constant should enhance robustness, but make them harder to learn with classical loss…

We propose a Gaussian variational inference framework for the motion planning problem. In this framework, motion planning is formulated as an optimization over the distribution of the trajectories to approximate the desired trajectory…

This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to…

Point sets matching problems can be handled by optimal transport. The mechanism behind it is that optimal transport recovers the point-to-point correspondence associated with the least curl deformation. Optimal transport is a special form…

This article presents a general approximation-theoretic framework to analyze measure transport algorithms for probabilistic modeling. A primary motivating application for such algorithms is sampling -- a central task in statistical…

This paper proposes an optimization-based approach to predict trajectories of autonomous race cars. We assume that the observed trajectory is the result of an optimization problem that trades off path progress against acceleration and jerk…

A data-driven formulation of the optimal transport problem is presented and solved using adaptively refined meshes to decompose the problem into a sequence of finite linear programming problems. Both the marginal distributions and their…

Unsupervised deep learning approaches have recently become one of the crucial research areas in imaging owing to their ability to learn expressive and powerful reconstruction operators even when paired high-quality training data is scarcely…

In this work, we develop an optimal transport (OT) based framework to select informative prototypical examples that best represent a given target dataset. Summarizing a given target dataset via representative examples is an important…

We address the problem of identifying the dynamical law governing the evolution of a population of indistinguishable particles, when only aggregate distributions at successive times are observed. Assuming a Markovian evolution on a discrete…

This paper introduces Wasserstein variational inference, a new form of approximate Bayesian inference based on optimal transport theory. Wasserstein variational inference uses a new family of divergences that includes both f-divergences and…

While progress has been made in understanding the robustness of machine learning classifiers to test-time adversaries (evasion attacks), fundamental questions remain unresolved. In this paper, we use optimal transport to characterize the…

A memetic framework for optimal inverse design is proposed by combining a local gradient-based procedure and a robust global scheme. The procedure is based on method-of-moments matrices and does not demand full inversion of a system matrix.…

Optimal transport is widely used in pure and applied mathematics to find probabilistic solutions to hard combinatorial matching problems. We extend the Wasserstein metric and other elements of optimal transport from the matching of sets to…

The power and flexibility of Optimal Transport (OT) have pervaded a wide spectrum of problems, including recent Machine Learning challenges such as unsupervised domain adaptation. Its essence of quantitatively relating two probability…

In robotics and multi-agent systems, fleets of autonomous agents often operate in subtly different environments while pursuing a common high-level objective. Directly pooling their data to learn a shared reward function is typically…

The empirical optimal transport (OT) cost between two probability measures from random data is a fundamental quantity in transport based data analysis. In this work, we derive novel guarantees for its convergence rate when the involved…

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.…