A survey of the Schrödinger problem and some of its connections with optimal transport
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In this paper, the authors present the Schrodinger problem and some of its connections with optimal transport, and give a user's guide to the problem and a survey of the related literature.Abstract:
This article is aimed at presenting the Schrodinger problem and some of its connections with optimal transport. We hope that it can be used as a basic user's guide to Schrodinger problem. We also give a survey of the related literature. In addition, some new results are proved.read more
Citations
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Journal ArticleDOI
Convergence of Probability Measures
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
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Computational Optimal Transport
Gabriel Peyré,Marco Cuturi +1 more
TL;DR: This short book reviews OT with a bias toward numerical methods and their applications in data sciences, and sheds lights on the theoretical properties of OT that make it particularly useful for some of these applications.
Journal ArticleDOI
Iterative Bregman Projections for Regularized Transportation Problems
TL;DR: In this article, a general numerical framework to approximate so-lutions to linear programs related to optimal transport is presented, where the set of linear constraints can be split in an intersection of a few simple constraints, for which the projections can be computed in closed form.
Posted Content
Iterative Bregman Projections for Regularized Transportation Problems
TL;DR: It is shown that for many problems related to optimal transport, the set of linear constraints can be split in an intersection of a few simple constraints, for which the projections can be computed in closed form.
Journal ArticleDOI
Optimal-Transport Analysis of Single-Cell Gene Expression Identifies Developmental Trajectories in Reprogramming.
Geoffrey Schiebinger,Geoffrey Schiebinger,Jian Shu,Jian Shu,Marcin Tabaka,Brian Cleary,Brian Cleary,Vidya Subramanian,Aryeh Solomon,Joshua Gould,Siyan Liu,Siyan Liu,Stacie Lin,Stacie Lin,Peter Berube,Lia Lee,Jenny Chen,Jenny Chen,Justin Brumbaugh,Philippe Rigollet,Konrad Hochedlinger,Rudolf Jaenisch,Aviv Regev,Aviv Regev,Aviv Regev,Eric S. Lander,Eric S. Lander,Eric S. Lander +27 more
TL;DR: Waddington-OT is introduced, an approach for studying developmental time courses to infer ancestor-descendant fates and model the regulatory programs that underlie them that sheds light on the process and outcome of reprogramming and provides a framework applicable to diverse temporal processes in biology.
References
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Book
Convergence of Probability Measures
TL;DR: Weak Convergence in Metric Spaces as discussed by the authors is one of the most common modes of convergence in metric spaces, and it can be seen as a form of weak convergence in metric space.
Book
Quantum Mechanics and Path Integrals
TL;DR: Au sommaire as discussed by the authors developed the concepts of quantum mechanics with special examples and developed the perturbation method in quantum mechanics and the variational method for probability problems in quantum physics.
Book
Continuous martingales and Brownian motion
Daniel Revuz,Marc Yor +1 more
TL;DR: In this article, the authors present a comprehensive survey of the literature on limit theorems in distribution in function spaces, including Girsanov's Theorem, Bessel Processes, and Ray-Knight Theorem.
Journal ArticleDOI
Convergence of Probability Measures
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.