Projection‐based techniques for high‐dimensional optimal transport problems
Optimal transport (OT) methods seek a transformation map (or plan) between two probability
measures, such that the transformation has the minimum transportation cost. Such a …
measures, such that the transformation has the minimum transportation cost. Such a …
Automatic text evaluation through the lens of Wasserstein barycenters
A new metric\texttt {BaryScore} to evaluate text generation based on deep contextualized
embeddings eg, BERT, Roberta, ELMo) is introduced. This metric is motivated by a new …
embeddings eg, BERT, Roberta, ELMo) is introduced. This metric is motivated by a new …
Integrating efficient optimal transport and functional maps for unsupervised shape correspondence learning
In the realm of computer vision and graphics accurately establishing correspondences
between geometric 3D shapes is pivotal for applications like object tracking registration …
between geometric 3D shapes is pivotal for applications like object tracking registration …
On the complexity of approximating multimarginal optimal transport
We study the complexity of approximating the multimarginal optimal transport (MOT)
distance, a generalization of the classical optimal transport distance, considered here …
distance, a generalization of the classical optimal transport distance, considered here …
Multi-marginal optimal transport and probabilistic graphical models
We study multi-marginal optimal transport problems from a probabilistic graphical model
perspective. We point out an elegant connection between the two when the underlying cost …
perspective. We point out an elegant connection between the two when the underlying cost …
Averaging on the Bures-Wasserstein manifold: dimension-free convergence of gradient descent
J Altschuler, S Chewi, PR Gerber… - Advances in Neural …, 2021 - proceedings.neurips.cc
We study first-order optimization algorithms for computing the barycenter of Gaussian
distributions with respect to the optimal transport metric. Although the objective is …
distributions with respect to the optimal transport metric. Although the objective is …
Wasserstein barycenters are NP-hard to compute
JM Altschuler, E Boix-Adsera - SIAM Journal on Mathematics of Data Science, 2022 - SIAM
Computing Wasserstein barycenters (aka optimal transport barycenters) is a fundamental
problem in geometry which has recently attracted considerable attention due to many …
problem in geometry which has recently attracted considerable attention due to many …
Hierarchical sliced wasserstein distance
Sliced Wasserstein (SW) distance has been widely used in different application scenarios
since it can be scaled to a large number of supports without suffering from the curse of …
since it can be scaled to a large number of supports without suffering from the curse of …
Revisiting sliced Wasserstein on images: From vectorization to convolution
The conventional sliced Wasserstein is defined between two probability measures that have
realizations as\textit {vectors}. When comparing two probability measures over images …
realizations as\textit {vectors}. When comparing two probability measures over images …
Amortized projection optimization for sliced Wasserstein generative models
Seeking informative projecting directions has been an important task in utilizing sliced
Wasserstein distance in applications. However, finding these directions usually requires an …
Wasserstein distance in applications. However, finding these directions usually requires an …