Description
"Learning from Low Rank Tensor Data A Random Tensor Theory Perspective" Mohamed El Amine Seddik, Malik Tiomoko, Alexis Decurninge, Maxime Guillaud, Maxim Panov (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.
Slides: https://www.auai.org/uai2023/oral_slides/432-oral-slides.pdf