Learning from Low Rank Tensor Data: A Random Tensor Theory Perspective
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
Text
Seddik et al. "Learning from Low Rank Tensor Data: A Random Tensor Theory Perspective." Uncertainty in Artificial Intelligence, 2023.Markdown
[Seddik et al. "Learning from Low Rank Tensor Data: A Random Tensor Theory Perspective." Uncertainty in Artificial Intelligence, 2023.](https://mlanthology.org/uai/2023/seddik2023uai-learning/)BibTeX
@inproceedings{seddik2023uai-learning,
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 = {Uncertainty in Artificial Intelligence},
year = {2023},
pages = {1858-1867},
volume = {216},
url = {https://mlanthology.org/uai/2023/seddik2023uai-learning/}
}