Corpus ID: 221802548

SISTA: Learning Optimal Transport Costs Under Sparsity Constraints

@article{Carlier2020SISTALO,
  title={SISTA: Learning Optimal Transport Costs Under Sparsity Constraints},
  author={G. Carlier and A. Dupuy and A. Galichon and Yifei Sun},
  journal={IZA Institute of Labor Economics Discussion Paper Series},
  year={2020}
}
  • G. Carlier, A. Dupuy, +1 author Yifei Sun
  • Published 2020
  • Mathematics, Computer Science
  • IZA Institute of Labor Economics Discussion Paper Series
In this paper, we describe a novel iterative procedure called SISTA to learn the underlying cost in optimal transport problems. SISTA is a hybrid between two classical methods, coordinate descent ("S"-inkhorn) and proximal gradient descent ("ISTA"). It alternates between a phase of exact minimization over the transport potentials and a phase of proximal gradient descent over the parameters of the transport cost. We prove that this method converges linearly, and we illustrate on simulated… Expand
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References

SHOWING 1-10 OF 31 REFERENCES
Sinkhorn Distances: Lightspeed Computation of Optimal Transport
TLDR
This work smooths the classic optimal transport problem with an entropic regularization term, and shows that the resulting optimum is also a distance which can be computed through Sinkhorn's matrix scaling algorithm at a speed that is several orders of magnitude faster than that of transport solvers. Expand
Iterative Bregman Projections for Regularized Transportation Problems
TLDR
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. Expand
Estimating Matching Affinity Matrix under Low-Rank Constraints
In this paper, we address the problem of estimating transport surplus (a.k.a. matching affinity) in high dimensional optimal transport problems. Classical optimal transport theory species theExpand
Estimating Matching Affinity Matrix Under Low-Rank Constraints
In this paper, we address the problem of estimating transport surplus (a.k.a. matching affinity) in high dimensional optimal transport problems. Classical optimal transport theory specifies theExpand
Computational Optimal Transport
TLDR
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. Expand
Optimal Transport Methods in Economics
Optimal Transport Methods in Economics is the first textbook on the subject written especially for students and researchers in economics. Optimal transport theory is used widely to solve problems inExpand
Ground metric learning
TLDR
The problem of learning the ground metric is formulated as the minimization of the difference of two convex polyhedral functions over a convex set of metric matrices and it is shown that this approach is useful both for retrieval and binary/multiclass classification tasks. Expand
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
TLDR
A new fast iterative shrinkage-thresholding algorithm (FISTA) which preserves the computational simplicity of ISTA but with a global rate of convergence which is proven to be significantly better, both theoretically and practically. Expand
A review of matrix scaling and Sinkhorn's normal form for matrices and positive maps
Given a nonnegative matrix $A$, can you find diagonal matrices $D_1,~D_2$ such that $D_1AD_2$ is doubly stochastic? The answer to this question is known as Sinkhorn's theorem. It has been proved withExpand
Metric Learning: A Survey
  • B. Kulis
  • Computer Science
  • Found. Trends Mach. Learn.
  • 2013
TLDR
Metric Learning: A Review presents an overview of existing research in this topic, including recent progress on scaling to high-dimensional feature spaces and to data sets with an extremely large number of data points. Expand
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