# Subspace Detours: Building Transport Plans that are Optimal on Subspace Projections

@inproceedings{Muzellec2019SubspaceDB, title={Subspace Detours: Building Transport Plans that are Optimal on Subspace Projections}, author={Boris Muzellec and Marco Cuturi}, booktitle={NeurIPS}, year={2019} }

Computing optimal transport (OT) between measures in high dimensions is doomed by the curse of dimensionality. A popular approach to avoid this curse is to project input measures on lower-dimensional subspaces (1D lines in the case of sliced Wasserstein distances), solve the OT problem between these reduced measures, and settle for the Wasserstein distance between these reductions, rather than that between the original measures. This approach is however difficult to extend to the case in which… Expand

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#### 12 Citations

Efficient estimates of optimal transport via low-dimensional embeddings Conference Submissions

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Optimal transport distances (OT) have been widely used in recent work in Machine Learning as ways to compare probability distributions. These are costly to compute when the data lives in high… Expand

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O C ] 1 7 O ct 2 01 9 OPTIMAL TRANSPORT AND BARYCENTERS FOR DENDRITIC MEASURES

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We introduce and study a variant of the Wasserstein distance on the space of probability measures, specially designed to deal with measures whose support has a dendritic, or treelike structure with a… Expand

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A Review on Modern Computational Optimal Transport Methods with Applications in Biomedical Research

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This review presents some cutting-edge computational optimal transport methods with a focus on the regularization- based methods and the projection-based methods and discusses their real-world applications in biomedical research. Expand

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The proposed Batch of Mini-batches Optimal Transport (BoMb-OT) is a novel mini-batching scheme for optimal transport that can be formulated as a well-defined distance on the space of probability measures and provides a better objective loss than m-OT for doing approximate Bayesian computation, estimating parameters of interest in parametric generative models, and learning non-parametricGenerative models with gradient flow. Expand

Augmented Sliced Wasserstein Distances

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