Performance of Rank-One Tensor Approximation on Incomplete Data
arXiv:2504.07818v1 Announce Type: new
Abstract: We are interested in the estimation of a rank-one tensor signal when only a portion $varepsilon$ 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.
Abstract: We are interested in the estimation of a rank-one tensor signal when only a portion $varepsilon$ 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.
Hugo Lebeau
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