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Talking about Optimal Transport
In this session, we have the pleasure of hosting Luigi Ambrosio, a professor at the Scuola Normale Superiore in Pisa, Italy, as our guest. Professor...
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Applications of Optimal Transport Techniques
Our goal in this Chapter is to exploit the link between the least gradient problem and the Monge-Kantorovich optimal transport problem presented in...
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Optimal Transport for Generative Models
Optimal transport plays a fundamental role in deep learning. Natural data sets have intrinsic patterns, which can be summarized as the manifold...
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Computational Optimal Transport
The optimal transport (OT) problem is a classical optimization problem having the form of linear programming. Machine learning applications put...
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Robust Risk Management via Multi-marginal Optimal Transport
We study the problem of maximizing a spectral risk measure of a given output function which depends on several underlying variables, whose individual...
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Conversations on Optimal Transport
This work is closely tied to the renowned mathematics textbook series known as UNITEXT, tailored for university students pursuing bachelor’s or...
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Moment-SoS methods for optimal transport problems
Most common optimal transport (OT) solvers are currently based on an approximation of underlying measures by discrete measures. However, it is...
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Efficient and Exact Multimarginal Optimal Transport with Pairwise Costs
We address the numerical solution to multimarginal optimal transport (MMOT) with pairwise costs. MMOT, as a natural extension from the classical...
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Hypergraph co-optimal transport: metric and categorical properties
Hypergraphs capture multi-way relationships in data, and they have consequently seen a number of applications in higher-order network analysis,...
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Optimal Transport, Fields Medals and beyond
Welcome to the Springer Math Podcast. This month, we’re delighted to host Alessio Figalli, the Director of the Institute for Mathematical Research at...
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Algorithms for Euclidean-Regularised Optimal Transport
This paper addresses the Optimal Transport problem, which is regularized by the square of Euclidean...
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Entropy martingale optimal transport and nonlinear pricing–hedging duality
The objective of this paper is to develop a duality between a novel entropy martingale optimal transport (EMOT) problem and an associated...
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A general framework for multi-marginal optimal transport
We establish a general condition on the cost function to obtain uniqueness and Monge solutions in the multi-marginal optimal transport problem, under...
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From Optimal Transport to Discrepancy
A common way to quantify the “distance” between measures is via their discrepancy, also known as maximum mean discrepancy (MMD). Discrepancies are...
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Optimal Transport and Applications to Geometric Optics
This book concerns the theory of optimal transport (OT) and its applications to solving problems in geometric optics. It is a self-contained...
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Visualizing Fluid Flows via Regularized Optimal Mass Transport with Applications to Neuroscience
The regularized optimal mass transport (rOMT) problem adds a diffusion term to the continuity equation in the original dynamic formulation of the...
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When optimal transport meets information geometry
Information geometry and optimal transport are two distinct geometric frameworks for modeling families of probability measures. During the recent...
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Equivalence with an Optimal Transport Problem in Two Dimensions
In two dimensions, the least gradient problem can be interpreted in several different ways. In this Chapter, we focus on the equivalence between the...
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Numerical Optimal Transport from 1D to 2D Using a Non-local Monge-Ampère Equation
We consider the numerical solution of the optimal transport problem between densities that are supported on sets of unequal dimension. Recent work by...
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Heterogeneous gradient flows in the topology of fibered optimal transport
We introduce an optimal transport topology on the space of probability measures over a fiber bundle, which penalizes the transport cost from one...
