AISTATS 2022poster22 citations
Sobolev Transport: A Scalable Metric for Probability Measures with Graph Metrics
Tam Le, Truyen Nguyen, Dinh Phung, Viet Anh Nguyen
Abstract
Optimal transport (OT) is a popular measure to compare probability distributions. However, OT suffers a few drawbacks such as (i) a high complexity for computation, (ii) indefiniteness which limits its applicability to kernel machines. In this work, we consider probability measures supported on a graph metric space and propose a novel Sobolev transport metric. We show that the Sobolev transport metric yields a
BibTeX
@InProceedings{pmlr-v151-le22b,
title = { Sobolev Transport: A Scalable Metric for Probability Measures with Graph Metrics },
author = {Le, Tam and Nguyen, Truyen and Phung, Dinh and Anh Nguyen, Viet},
booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics},
pages = {9844--9868},
year = {2022},
editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel},
volume = {151},
series = {Proceedings of Machine Learning Research},
month = {28--30 Mar},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v151/le22b/le22b.pdf},
url = {https://proceedings.mlr.press/v151/le22b.html},
abstract = { Optimal transport (OT) is a popular measure to compare probability distributions. However, OT suffers a few drawbacks such as (i) a high complexity for computation, (ii) indefiniteness which limits its applicability to kernel machines. In this work, we consider probability measures supported on a graph metric space and propose a novel Sobolev transport metric. We show that the Sobolev transport metric yields a