当前位置: X-MOL 学术arXiv.cs.CC › 论文详情
Computational Hardness and Fast Algorithm for Fixed-Support Wasserstein Barycenter
arXiv - CS - Computational Complexity Pub Date : 2020-02-12 , DOI: arxiv-2002.04783
Tianyi Lin; Nhat Ho; Xi Chen; Marco Cuturi; Michael I. Jordan

We study in this paper the fixed-support Wasserstein barycenter problem (FS-WBP), which consists in computing the Wasserstein barycenter of $m$ discrete probability measures supported on a finite metric space of size $n$. We show first that the constraint matrix arising from the standard linear programming (LP) representation of the FS-WBP is $\textit{not totally unimodular}$ when $m \geq 3$ and $n \geq 3$. This result answers an open question pertaining to the relationship between the FS-WBP and the minimum-cost flow (MCF) problem since it therefore proves that the FS-WBP in the standard LP form is not a MCF problem when $m \geq 3$ and $n \geq 3$. We also develop a provably fast \textit{deterministic} variant of the celebrated iterative Bregman projection (IBP) algorithm, named \textsc{FastIBP} algorithm, with the complexity bound of $\widetilde{O}(mn^{7/3}\varepsilon^{-4/3})$ where $\varepsilon \in (0, 1)$ is the tolerance. This complexity bound is better than the best known complexity bound of $\widetilde{O}(mn^2\varepsilon^{-2})$ from the IBP algorithm in terms of $\varepsilon$, and that of $\widetilde{O}(mn^{5/2}\varepsilon^{-1})$ from other accelerated algorithms in terms of $n$. Finally, we conduct extensive experiments with both synthetic and real data and demonstrate the favorable performance of the \textsc{FastIBP} algorithm in practice.
更新日期:2020-02-12

 

全部期刊列表>>
物理学研究前沿热点精选期刊推荐
chemistry
《自然》编辑与您分享如何成为优质审稿人-信息流
欢迎报名注册2020量子在线大会
化学领域亟待解决的问题
材料学研究精选新
GIANT
自然职场线上招聘会
ACS ES&T Engineering
ACS ES&T Water
ACS Publications填问卷
屿渡论文,编辑服务
阿拉丁试剂right
南昌大学
王辉
南方科技大学
刘天飞
隐藏1h前已浏览文章
课题组网站
新版X-MOL期刊搜索和高级搜索功能介绍
ACS材料视界
天合科研
x-mol收录
X-MOL
苏州大学
廖矿标
深圳湾
试剂库存
down
wechat
bug