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Conference Papers Year : 2023

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.
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hal-04184112 , version 1 (21-08-2023)

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  • HAL Id : hal-04184112 , version 1

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Mohamed El Amine Seddik, Malik Tiomoko, Alexis Decurninge, Maxim Panov, Maxime Guillaud. Learning from Low Rank Tensor Data: A Random Tensor Theory Perspective. Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, Jul 2023, Pittsburgh, PA (USA), United States. ⟨hal-04184112⟩
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