Learning from Low Rank Tensor Data: A Random Tensor Theory Perspective

Mohamed El Amine Seddik, Malik Tiomoko, Alexis Decurninge, Maxim Panov, Maxime Gauillaud
Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, PMLR 216:1858-1867, 2023.

Abstract

Under a simplified data model, this paper provides a theoretical analysis of learning from data that have an underlying low-rank tensor structure in both supervised and unsupervised settings. For the supervised setting, we provide an analysis of a Ridge classifier (with high regularization parameter) with and without knowledge of the low-rank structure of the data. Our results quantify analytically the gain in misclassification errors achieved by exploiting the low-rank structure for denoising purposes, as opposed to treating data as mere vectors. We further provide a similar analysis in the context of clustering, thereby quantifying the exact performance gap between tensor methods and standard approaches which treat data as simple vectors.

Cite this Paper

BibTeX
@InProceedings{pmlr-v216-seddik23a, title = {Learning from Low Rank Tensor Data: A Random Tensor Theory Perspective}, author = {Seddik, Mohamed El Amine and Tiomoko, Malik and Decurninge, Alexis and Panov, Maxim and Gauillaud, Maxime}, booktitle = {Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence}, pages = {1858--1867}, year = {2023}, editor = {Evans, Robin J. and Shpitser, Ilya}, volume = {216}, series = {Proceedings of Machine Learning Research}, month = {31 Jul--04 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v216/seddik23a/seddik23a.pdf}, url = {https://proceedings.mlr.press/v216/seddik23a.html}, abstract = {Under a simplified data model, this paper provides a theoretical analysis of learning from data that have an underlying low-rank tensor structure in both supervised and unsupervised settings. For the supervised setting, we provide an analysis of a Ridge classifier (with high regularization parameter) with and without knowledge of the low-rank structure of the data. Our results quantify analytically the gain in misclassification errors achieved by exploiting the low-rank structure for denoising purposes, as opposed to treating data as mere vectors. We further provide a similar analysis in the context of clustering, thereby quantifying the exact performance gap between tensor methods and standard approaches which treat data as simple vectors.} }
Endnote
%0 Conference Paper %T Learning from Low Rank Tensor Data: A Random Tensor Theory Perspective %A Mohamed El Amine Seddik %A Malik Tiomoko %A Alexis Decurninge %A Maxim Panov %A Maxime Gauillaud %B Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2023 %E Robin J. Evans %E Ilya Shpitser %F pmlr-v216-seddik23a %I PMLR %P 1858--1867 %U https://proceedings.mlr.press/v216/seddik23a.html %V 216 %X Under a simplified data model, this paper provides a theoretical analysis of learning from data that have an underlying low-rank tensor structure in both supervised and unsupervised settings. For the supervised setting, we provide an analysis of a Ridge classifier (with high regularization parameter) with and without knowledge of the low-rank structure of the data. Our results quantify analytically the gain in misclassification errors achieved by exploiting the low-rank structure for denoising purposes, as opposed to treating data as mere vectors. We further provide a similar analysis in the context of clustering, thereby quantifying the exact performance gap between tensor methods and standard approaches which treat data as simple vectors.
APA
Seddik, M.E.A., Tiomoko, M., Decurninge, A., Panov, M. & Gauillaud, M.. (2023). Learning from Low Rank Tensor Data: A Random Tensor Theory Perspective. Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 216:1858-1867 Available from https://proceedings.mlr.press/v216/seddik23a.html.

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