Learning from Multiway Data: Simple and Efficient Tensor Regression

Rose Yu, Yan Liu
Proceedings of The 33rd International Conference on Machine Learning, PMLR 48:373-381, 2016.

Abstract

Tensor regression has shown to be advantageous in learning tasks with multi-directional relatedness. Given massive multiway data, traditional methods are often too slow to operate on or suffer from memory bottleneck. In this paper, we introduce subsampled tensor projected gradient to solve the problem. Our algorithm is impressively simple and efficient. It is built upon projected gradient method with fast tensor power iterations, leveraging randomized sketching for further acceleration. Theoretical analysis shows that our algorithm converges to the correct solution in fixed number of iterations. The memory requirement grows linearly with the size of the problem. We demonstrate superior empirical performance on both multi-linear multi-task learning and spatio-temporal applications.

Cite this Paper

BibTeX
@InProceedings{pmlr-v48-yu16, title = {Learning from Multiway Data: Simple and Efficient Tensor Regression}, author = {Yu, Rose and Liu, Yan}, booktitle = {Proceedings of The 33rd International Conference on Machine Learning}, pages = {373--381}, year = {2016}, editor = {Balcan, Maria Florina and Weinberger, Kilian Q.}, volume = {48}, series = {Proceedings of Machine Learning Research}, address = {New York, New York, USA}, month = {20--22 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v48/yu16.pdf}, url = {https://proceedings.mlr.press/v48/yu16.html}, abstract = {Tensor regression has shown to be advantageous in learning tasks with multi-directional relatedness. Given massive multiway data, traditional methods are often too slow to operate on or suffer from memory bottleneck. In this paper, we introduce subsampled tensor projected gradient to solve the problem. Our algorithm is impressively simple and efficient. It is built upon projected gradient method with fast tensor power iterations, leveraging randomized sketching for further acceleration. Theoretical analysis shows that our algorithm converges to the correct solution in fixed number of iterations. The memory requirement grows linearly with the size of the problem. We demonstrate superior empirical performance on both multi-linear multi-task learning and spatio-temporal applications.} }
Endnote
%0 Conference Paper %T Learning from Multiway Data: Simple and Efficient Tensor Regression %A Rose Yu %A Yan Liu %B Proceedings of The 33rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2016 %E Maria Florina Balcan %E Kilian Q. Weinberger %F pmlr-v48-yu16 %I PMLR %P 373--381 %U https://proceedings.mlr.press/v48/yu16.html %V 48 %X Tensor regression has shown to be advantageous in learning tasks with multi-directional relatedness. Given massive multiway data, traditional methods are often too slow to operate on or suffer from memory bottleneck. In this paper, we introduce subsampled tensor projected gradient to solve the problem. Our algorithm is impressively simple and efficient. It is built upon projected gradient method with fast tensor power iterations, leveraging randomized sketching for further acceleration. Theoretical analysis shows that our algorithm converges to the correct solution in fixed number of iterations. The memory requirement grows linearly with the size of the problem. We demonstrate superior empirical performance on both multi-linear multi-task learning and spatio-temporal applications.
RIS
TY - CPAPER TI - Learning from Multiway Data: Simple and Efficient Tensor Regression AU - Rose Yu AU - Yan Liu BT - Proceedings of The 33rd International Conference on Machine Learning DA - 2016/06/11 ED - Maria Florina Balcan ED - Kilian Q. Weinberger ID - pmlr-v48-yu16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 48 SP - 373 EP - 381 L1 - http://proceedings.mlr.press/v48/yu16.pdf UR - https://proceedings.mlr.press/v48/yu16.html AB - Tensor regression has shown to be advantageous in learning tasks with multi-directional relatedness. Given massive multiway data, traditional methods are often too slow to operate on or suffer from memory bottleneck. In this paper, we introduce subsampled tensor projected gradient to solve the problem. Our algorithm is impressively simple and efficient. It is built upon projected gradient method with fast tensor power iterations, leveraging randomized sketching for further acceleration. Theoretical analysis shows that our algorithm converges to the correct solution in fixed number of iterations. The memory requirement grows linearly with the size of the problem. We demonstrate superior empirical performance on both multi-linear multi-task learning and spatio-temporal applications. ER -
APA
Yu, R. & Liu, Y.. (2016). Learning from Multiway Data: Simple and Efficient Tensor Regression. Proceedings of The 33rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 48:373-381 Available from https://proceedings.mlr.press/v48/yu16.html.

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