Différences
Ci-dessous, les différences entre deux révisions de la page.
| Les deux révisions précédentes Révision précédente | |||
| mega:seminaire [2026/04/21 11:42] – Raphaël BUTEZ | mega:seminaire [2026/04/21 11:42] (Version actuelle) – Raphaël BUTEZ | ||
|---|---|---|---|
| Ligne 29: | Ligne 29: | ||
| Abstract: This work presents a comprehensive understanding of the estimation of a planted low-rank signal from a general spiked tensor model near the computational threshold. Relying on standard tools from the theory of large random matrices, we characterize the large-dimensional spectral behavior of the unfoldings of the data tensor and exhibit relevant signal-to-noise ratios governing the detectability of the principal directions of the signal. These results allow to accurately predict the reconstruction performance of truncated multilinear SVD (MLSVD) in the non-trivial regime. This is particularly important since it serves as an initialization of the higher-order orthogonal iteration (HOOI) scheme, whose convergence to the best low-multilinear-rank approximation depends entirely on its initialization. We give a sufficient condition for the convergence of HOOI and show that the number of iterations before convergence tends to 1 in the large-dimensional limit. | Abstract: This work presents a comprehensive understanding of the estimation of a planted low-rank signal from a general spiked tensor model near the computational threshold. Relying on standard tools from the theory of large random matrices, we characterize the large-dimensional spectral behavior of the unfoldings of the data tensor and exhibit relevant signal-to-noise ratios governing the detectability of the principal directions of the signal. These results allow to accurately predict the reconstruction performance of truncated multilinear SVD (MLSVD) in the non-trivial regime. This is particularly important since it serves as an initialization of the higher-order orthogonal iteration (HOOI) scheme, whose convergence to the best low-multilinear-rank approximation depends entirely on its initialization. We give a sufficient condition for the convergence of HOOI and show that the number of iterations before convergence tends to 1 in the large-dimensional limit. | ||
| - | * 16h00-16h30: | + | * 16h00-16h30: |
| - | * 16h30-17h: Exposé court | + | * 16h30-17h00: Exposé court ouvert à contribution (date limite 01/05/2026) |