Scaling algorithms for unbalanced optimal transport problems

By Lénaïc Chizat, G. Peyr'e, Bernhard Schmitzer, François-Xavier Vialard. Mathematics of Computation, 2017

415 citations recorded by the source corpus.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3ecac5a84b7d8d8d15b25ecbd022ae353ad25c40

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In Applied Mathematics

In Statistics and Probability

Citations in the corpus

Entropic regularization of continuous optimal transport problems (2019, background): “Furthermore, [15] analyzes the problem (for unbalanced transport, i.”
Wasserstein Barycenter Model Ensembling (2019, methodology): “Wasserstein distances were originally defined between normalized probability vectors (Balanced OT) (Villani, 2008; Peyré & Cuturi, 2017), but they have been extended to deal with unnormalized measures and this problem is referred to as unbalanced OT (Chizat et al., 2018; Frogner et al., 2015).”
Sinkhorn Barycenters with Free Support via Frank-Wolfe Algorithm (2019, background): “Then, the dual problem of (1), in the sense of Fenchel-Rockafellar, is (see [10, 21])”
Optimal-transport analysis of single-cell gene expression identifies developmental trajectories in reprogramming (2019, positive): “Leveraging techniques from unbalanced transport (Chizat et al., 2018), we estimate cellular growth and death rates based on prior estimates from signatures of cellular proliferation and apoptosis (Methods S1, STAR Methods).”
Screening cell–cell communication in spatial transcriptomics via collective optimal transport (2023, methodology): “Specifically, unbalanced optimal transport 38 in its common form uses Kullback–Leibler divergence as a soft constraint on marginal distribution preservation.”
Fast geometric learning with symbolic matrices (2020, neutral): “For the sake of numerical stability, we use symmetric updates [70] and perform all computations in the logarithmic domain [23].”
Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning (2019, methodology): “When augmented with an entropic regularization term, for instance, the finite-dimensional transportation problem can be solved quickly by using Sinkhorn’s algorithm [22, 26, 52, 80, 81, 94, 102].”
Inferring spatial and signaling relationships between cells from single cell transcriptomic data (2020, methodology): “These matrices are fed to an unbalanced 21 and structured 22 optimal transport algorithm (Eq.”