Learning from Low Rank Tensor Data: A Random Tensor Theory Perspective
Mohamed El Amine Seddik, Malik Tiomoko, Alexis Decurninge, Maxim Panov, Maxime Gauillaud
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.
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.}
}