Fast Sampling-Based Sketches for Tensors

William Joseph Swartworth, David Woodruff
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:47378-47395, 2024.

Abstract

We introduce a new approach for applying sampling-based sketches to two and three mode tensors. We illustrate our technique to construct sketches for the classical problems of $\ell_0$ sampling and producing $\ell_1$ embeddings. In both settings we achieve sketches that can be applied to a rank one tensor in $(\mathbb{R}^d)^{\otimes q}$ (for $q=2,3$) in time scaling with $d$ rather than $d^2$ or $d^3$. Our main idea is a particular sampling construction based on fast convolution which allows us to quickly compute sums over sufficiently random subsets of tensor entries.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-swartworth24a, title = {Fast Sampling-Based Sketches for Tensors}, author = {Swartworth, William Joseph and Woodruff, David}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {47378--47395}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/swartworth24a/swartworth24a.pdf}, url = {https://proceedings.mlr.press/v235/swartworth24a.html}, abstract = {We introduce a new approach for applying sampling-based sketches to two and three mode tensors. We illustrate our technique to construct sketches for the classical problems of $\ell_0$ sampling and producing $\ell_1$ embeddings. In both settings we achieve sketches that can be applied to a rank one tensor in $(\mathbb{R}^d)^{\otimes q}$ (for $q=2,3$) in time scaling with $d$ rather than $d^2$ or $d^3$. Our main idea is a particular sampling construction based on fast convolution which allows us to quickly compute sums over sufficiently random subsets of tensor entries.} }
Endnote
%0 Conference Paper %T Fast Sampling-Based Sketches for Tensors %A William Joseph Swartworth %A David Woodruff %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-swartworth24a %I PMLR %P 47378--47395 %U https://proceedings.mlr.press/v235/swartworth24a.html %V 235 %X We introduce a new approach for applying sampling-based sketches to two and three mode tensors. We illustrate our technique to construct sketches for the classical problems of $\ell_0$ sampling and producing $\ell_1$ embeddings. In both settings we achieve sketches that can be applied to a rank one tensor in $(\mathbb{R}^d)^{\otimes q}$ (for $q=2,3$) in time scaling with $d$ rather than $d^2$ or $d^3$. Our main idea is a particular sampling construction based on fast convolution which allows us to quickly compute sums over sufficiently random subsets of tensor entries.
APA
Swartworth, W.J. & Woodruff, D.. (2024). Fast Sampling-Based Sketches for Tensors. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:47378-47395 Available from https://proceedings.mlr.press/v235/swartworth24a.html.

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