More Efficient Sampling for Tensor Decomposition With Worst-Case Guarantees

Osman Asif Malik
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:14887-14917, 2022.

Abstract

Recent papers have developed alternating least squares (ALS) methods for CP and tensor ring decomposition with a per-iteration cost which is sublinear in the number of input tensor entries for low-rank decomposition. However, the per-iteration cost of these methods still has an exponential dependence on the number of tensor modes when parameters are chosen to achieve certain worst-case guarantees. In this paper, we propose sampling-based ALS methods for the CP and tensor ring decompositions whose cost does not have this exponential dependence, thereby significantly improving on the previous state-of-the-art. We provide a detailed theoretical analysis and also apply the methods in a feature extraction experiment.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-malik22a, title = {More Efficient Sampling for Tensor Decomposition With Worst-Case Guarantees}, author = {Malik, Osman Asif}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {14887--14917}, 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/malik22a/malik22a.pdf}, url = {https://proceedings.mlr.press/v162/malik22a.html}, abstract = {Recent papers have developed alternating least squares (ALS) methods for CP and tensor ring decomposition with a per-iteration cost which is sublinear in the number of input tensor entries for low-rank decomposition. However, the per-iteration cost of these methods still has an exponential dependence on the number of tensor modes when parameters are chosen to achieve certain worst-case guarantees. In this paper, we propose sampling-based ALS methods for the CP and tensor ring decompositions whose cost does not have this exponential dependence, thereby significantly improving on the previous state-of-the-art. We provide a detailed theoretical analysis and also apply the methods in a feature extraction experiment.} }
Endnote
%0 Conference Paper %T More Efficient Sampling for Tensor Decomposition With Worst-Case Guarantees %A Osman Asif Malik %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-malik22a %I PMLR %P 14887--14917 %U https://proceedings.mlr.press/v162/malik22a.html %V 162 %X Recent papers have developed alternating least squares (ALS) methods for CP and tensor ring decomposition with a per-iteration cost which is sublinear in the number of input tensor entries for low-rank decomposition. However, the per-iteration cost of these methods still has an exponential dependence on the number of tensor modes when parameters are chosen to achieve certain worst-case guarantees. In this paper, we propose sampling-based ALS methods for the CP and tensor ring decompositions whose cost does not have this exponential dependence, thereby significantly improving on the previous state-of-the-art. We provide a detailed theoretical analysis and also apply the methods in a feature extraction experiment.
APA
Malik, O.A.. (2022). More Efficient Sampling for Tensor Decomposition With Worst-Case Guarantees. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:14887-14917 Available from https://proceedings.mlr.press/v162/malik22a.html.

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