Quantum-Inspired Algorithms from Randomized Numerical Linear Algebra

Nadiia Chepurko, Kenneth Clarkson, Lior Horesh, Honghao Lin, David Woodruff
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:3879-3900, 2022.

Abstract

We create classical (non-quantum) dynamic data structures supporting queries for recommender systems and least-squares regression that are comparable to their quantum analogues. De-quantizing such algorithms has received a flurry of attention in recent years; we obtain sharper bounds for these problems. More significantly, we achieve these improvements by arguing that the previous quantum-inspired algorithms for these problems are doing leverage or ridge-leverage score sampling in disguise; these are powerful and standard techniques in randomized numerical linear algebra. With this recognition, we are able to employ the large body of work in numerical linear algebra to obtain algorithms for these problems that are simpler or faster (or both) than existing approaches. Our experiments demonstrate that the proposed data structures also work well on real-world datasets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-chepurko22a, title = {Quantum-Inspired Algorithms from Randomized Numerical Linear Algebra}, author = {Chepurko, Nadiia and Clarkson, Kenneth and Horesh, Lior and Lin, Honghao and Woodruff, David}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {3879--3900}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/chepurko22a/chepurko22a.pdf}, url = {https://proceedings.mlr.press/v162/chepurko22a.html}, abstract = {We create classical (non-quantum) dynamic data structures supporting queries for recommender systems and least-squares regression that are comparable to their quantum analogues. De-quantizing such algorithms has received a flurry of attention in recent years; we obtain sharper bounds for these problems. More significantly, we achieve these improvements by arguing that the previous quantum-inspired algorithms for these problems are doing leverage or ridge-leverage score sampling in disguise; these are powerful and standard techniques in randomized numerical linear algebra. With this recognition, we are able to employ the large body of work in numerical linear algebra to obtain algorithms for these problems that are simpler or faster (or both) than existing approaches. Our experiments demonstrate that the proposed data structures also work well on real-world datasets.} }
Endnote
%0 Conference Paper %T Quantum-Inspired Algorithms from Randomized Numerical Linear Algebra %A Nadiia Chepurko %A Kenneth Clarkson %A Lior Horesh %A Honghao Lin %A David Woodruff %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-chepurko22a %I PMLR %P 3879--3900 %U https://proceedings.mlr.press/v162/chepurko22a.html %V 162 %X We create classical (non-quantum) dynamic data structures supporting queries for recommender systems and least-squares regression that are comparable to their quantum analogues. De-quantizing such algorithms has received a flurry of attention in recent years; we obtain sharper bounds for these problems. More significantly, we achieve these improvements by arguing that the previous quantum-inspired algorithms for these problems are doing leverage or ridge-leverage score sampling in disguise; these are powerful and standard techniques in randomized numerical linear algebra. With this recognition, we are able to employ the large body of work in numerical linear algebra to obtain algorithms for these problems that are simpler or faster (or both) than existing approaches. Our experiments demonstrate that the proposed data structures also work well on real-world datasets.
APA
Chepurko, N., Clarkson, K., Horesh, L., Lin, H. & Woodruff, D.. (2022). Quantum-Inspired Algorithms from Randomized Numerical Linear Algebra. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:3879-3900 Available from https://proceedings.mlr.press/v162/chepurko22a.html.

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