Performance of Rank-One Tensor Approximation on Incomplete Data
Machine Learning
2025-06-30 v3 Machine Learning
Probability
Abstract
We are interested in the estimation of a rank-one tensor signal when only a portion of its noisy observation is available. We show that the study of this problem can be reduced to that of a random matrix model whose spectral analysis gives access to the reconstruction performance. These results shed light on and specify the loss of performance induced by an artificial reduction of the memory cost of a tensor via the deletion of a random part of its entries.
Cite
@article{arxiv.2504.07818,
title = {Performance of Rank-One Tensor Approximation on Incomplete Data},
author = {Hugo Lebeau},
journal= {arXiv preprint arXiv:2504.07818},
year = {2025}
}