Matches in SemOpenAlex for { <https://semopenalex.org/work/W2980665616> ?p ?o ?g. }
- W2980665616 abstract "We investigate the problem of pairwise multi-marginal optimal transport, that is, given a collection of probability distributions ${P_alpha}$ on a Polish space $mathcal{X}$, to find a coupling ${X_alpha}$, $X_alphasim P_alpha$, such that $mathbf{E}[c(X_alpha,X_beta)]le rinf_{Xsim P_alpha,Ysim P_beta}mathbf{E}[c(X,Y)]$ for all $alpha,beta$, where $c$ is a cost function and $rge1$. In other words, every pair $(X_alpha,X_beta)$ has an expected cost at most a factor of $r$ from its lowest possible value. This can be regarded as a locality sensitive hash function for probability distributions, and has applications such as robust and distributed computation of transport plans. It can also be considered as a bi-Lipschitz embedding of the collection of probability distributions into the space of random variables taking values on $mathcal{X}$. For $c(x,y)=Vert x-yVert_2^q$ on $mathbb{R}^n$, where $q>0$, we show that a finite $r$ is attainable if and only if either $n=1$ or $0<q<1$. As $ntoinfty$, the growth rate of the smallest possible $r$ is exactly $Theta(n^{q/2})$ if $0<q<1$. Hence, the metric space of probability distributions on $mathbb{R}^n$ with finite $q$-th absolute moments, $0<q<1$, with the earth mover's distance (or 1-Wasserstein distance) with respect to the snowflake metric $c(x,y)=Vert x-yVert_2^q$, is bi-Lipschitz embeddable into $L_1$ with distortion $O(n^{q/2})$. If we consider $c(x,y)=Vert x-yVert_2$ (i.e., $q=1$) on the grid $[0..s]^n$ instead of $mathbb{R}^n$, then $r=O(sqrt{n}log s)$ is attainable, which implies the embeddability of the space of probability distributions on $[0..s]^n$ into $L_1$ with distortion $O(sqrt{n}log s)$, and improves upon the $O(nlog s)$ result by Indyk and Thaper. The case of the discrete metric cost $c(x,y)=mathbf{1}{xneq y}$ and more general metric and ultrametric costs are also investigated." @default.
- W2980665616 created "2019-10-25" @default.
- W2980665616 creator A5013689450 @default.
- W2980665616 creator A5084702636 @default.
- W2980665616 date "2019-08-04" @default.
- W2980665616 modified "2023-09-27" @default.
- W2980665616 title "Pairwise Multi-marginal Optimal Transport and Embedding for Earth Mover's Distance" @default.
- W2980665616 cites W100489996 @default.
- W2980665616 cites W1525296983 @default.
- W2980665616 cites W1557499844 @default.
- W2980665616 cites W1605301393 @default.
- W2980665616 cites W1671098680 @default.
- W2980665616 cites W1967845895 @default.
- W2980665616 cites W1968036138 @default.
- W2980665616 cites W1977144601 @default.
- W2980665616 cites W1978210787 @default.
- W2980665616 cites W1981859328 @default.
- W2980665616 cites W2006208025 @default.
- W2980665616 cites W2011798344 @default.
- W2980665616 cites W2012833704 @default.
- W2980665616 cites W2027755860 @default.
- W2980665616 cites W2038921147 @default.
- W2980665616 cites W2046916388 @default.
- W2980665616 cites W2047176418 @default.
- W2980665616 cites W2052424080 @default.
- W2980665616 cites W2052449446 @default.
- W2980665616 cites W2052956617 @default.
- W2980665616 cites W2061130579 @default.
- W2980665616 cites W2062502830 @default.
- W2980665616 cites W2063491776 @default.
- W2980665616 cites W2082353536 @default.
- W2980665616 cites W2093126960 @default.
- W2980665616 cites W2095075176 @default.
- W2980665616 cites W2104648049 @default.
- W2980665616 cites W2105543801 @default.
- W2980665616 cites W2114493937 @default.
- W2980665616 cites W2148852318 @default.
- W2980665616 cites W2176446742 @default.
- W2980665616 cites W2183160839 @default.
- W2980665616 cites W2326587871 @default.
- W2980665616 cites W2401610261 @default.
- W2980665616 cites W2557537678 @default.
- W2980665616 cites W2886523564 @default.
- W2980665616 cites W2918257103 @default.
- W2980665616 cites W2962709856 @default.
- W2980665616 cites W2963044647 @default.
- W2980665616 cites W2963772459 @default.
- W2980665616 cites W2976022740 @default.
- W2980665616 cites W3009330671 @default.
- W2980665616 cites W3102152319 @default.
- W2980665616 cites W3103059853 @default.
- W2980665616 hasPublicationYear "2019" @default.
- W2980665616 type Work @default.
- W2980665616 sameAs 2980665616 @default.
- W2980665616 citedByCount "0" @default.
- W2980665616 crossrefType "posted-content" @default.
- W2980665616 hasAuthorship W2980665616A5013689450 @default.
- W2980665616 hasAuthorship W2980665616A5084702636 @default.
- W2980665616 hasConcept C105795698 @default.
- W2980665616 hasConcept C114614502 @default.
- W2980665616 hasConcept C118615104 @default.
- W2980665616 hasConcept C121332964 @default.
- W2980665616 hasConcept C122123141 @default.
- W2980665616 hasConcept C149441793 @default.
- W2980665616 hasConcept C154945302 @default.
- W2980665616 hasConcept C198043062 @default.
- W2980665616 hasConcept C21031990 @default.
- W2980665616 hasConcept C33923547 @default.
- W2980665616 hasConcept C41008148 @default.
- W2980665616 hasConcept C41608201 @default.
- W2980665616 hasConceptScore W2980665616C105795698 @default.
- W2980665616 hasConceptScore W2980665616C114614502 @default.
- W2980665616 hasConceptScore W2980665616C118615104 @default.
- W2980665616 hasConceptScore W2980665616C121332964 @default.
- W2980665616 hasConceptScore W2980665616C122123141 @default.
- W2980665616 hasConceptScore W2980665616C149441793 @default.
- W2980665616 hasConceptScore W2980665616C154945302 @default.
- W2980665616 hasConceptScore W2980665616C198043062 @default.
- W2980665616 hasConceptScore W2980665616C21031990 @default.
- W2980665616 hasConceptScore W2980665616C33923547 @default.
- W2980665616 hasConceptScore W2980665616C41008148 @default.
- W2980665616 hasConceptScore W2980665616C41608201 @default.
- W2980665616 hasLocation W29806656161 @default.
- W2980665616 hasOpenAccess W2980665616 @default.
- W2980665616 hasPrimaryLocation W29806656161 @default.
- W2980665616 hasRelatedWork W1538461340 @default.
- W2980665616 hasRelatedWork W1801609781 @default.
- W2980665616 hasRelatedWork W1990521888 @default.
- W2980665616 hasRelatedWork W1995926088 @default.
- W2980665616 hasRelatedWork W1999202288 @default.
- W2980665616 hasRelatedWork W2014291516 @default.
- W2980665616 hasRelatedWork W2018762455 @default.
- W2980665616 hasRelatedWork W2050187586 @default.
- W2980665616 hasRelatedWork W2161122706 @default.
- W2980665616 hasRelatedWork W2395851974 @default.
- W2980665616 hasRelatedWork W2789071508 @default.
- W2980665616 hasRelatedWork W2804942096 @default.
- W2980665616 hasRelatedWork W2952333464 @default.
- W2980665616 hasRelatedWork W2953155209 @default.
- W2980665616 hasRelatedWork W2965807866 @default.