What relations are reliably embeddable in Euclidean space?

Robi Bhattacharjee, Sanjoy Dasgupta
Proceedings of the 31st International Conference on Algorithmic Learning Theory, PMLR 117:174-195, 2020.

Abstract

We consider the problem of embedding a relation, represented as a directed graph, into Euclidean space. For three types of embeddings motivated by the recent literature on knowledge graphs, we obtain characterizations of which relations they are able to capture, as well as bounds on the minimal dimensionality and precision needed.

Cite this Paper

BibTeX
@InProceedings{pmlr-v117-bhattacharjee20a, title = {What relations are reliably embeddable in Euclidean space?}, author = {Bhattacharjee, Robi and Dasgupta, Sanjoy}, booktitle = {Proceedings of the 31st International Conference on Algorithmic Learning Theory}, pages = {174--195}, year = {2020}, editor = {Kontorovich, Aryeh and Neu, Gergely}, volume = {117}, series = {Proceedings of Machine Learning Research}, month = {08 Feb--11 Feb}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v117/bhattacharjee20a/bhattacharjee20a.pdf}, url = {https://proceedings.mlr.press/v117/bhattacharjee20a.html}, abstract = {We consider the problem of embedding a relation, represented as a directed graph, into Euclidean space. For three types of embeddings motivated by the recent literature on knowledge graphs, we obtain characterizations of which relations they are able to capture, as well as bounds on the minimal dimensionality and precision needed.} }
Endnote
%0 Conference Paper %T What relations are reliably embeddable in Euclidean space? %A Robi Bhattacharjee %A Sanjoy Dasgupta %B Proceedings of the 31st International Conference on Algorithmic Learning Theory %C Proceedings of Machine Learning Research %D 2020 %E Aryeh Kontorovich %E Gergely Neu %F pmlr-v117-bhattacharjee20a %I PMLR %P 174--195 %U https://proceedings.mlr.press/v117/bhattacharjee20a.html %V 117 %X We consider the problem of embedding a relation, represented as a directed graph, into Euclidean space. For three types of embeddings motivated by the recent literature on knowledge graphs, we obtain characterizations of which relations they are able to capture, as well as bounds on the minimal dimensionality and precision needed.
APA
Bhattacharjee, R. & Dasgupta, S.. (2020). What relations are reliably embeddable in Euclidean space?. Proceedings of the 31st International Conference on Algorithmic Learning Theory, in Proceedings of Machine Learning Research 117:174-195 Available from https://proceedings.mlr.press/v117/bhattacharjee20a.html.

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