The minimax rate for estimating d-th order moment tensors is sqrt(p/n) wedge 1, while low-degree evidence shows detection of vanishing cumulants is hard for n much less than p to the d/2, creating a reverse detection-estimation gap.
Revisit cp tensor decomposition: Statistical optimality and fast convergence.arXiv preprint arXiv:2505.23046, 2025a
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A three-phase alternating-update method for asymmetric tensor PCA achieves d to the power of k-minus-2 sample complexity with d-squared memory and improves when signal vectors align.
A functional tensor model with common invariant subspaces and RKHS-based estimation is introduced for dynamic multilayer networks to handle shared structures, temporal smoothness, and layer heterogeneity.
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Detection Is Harder Than Estimation in Certain Regimes: Inference for Moment and Cumulant Tensors
The minimax rate for estimating d-th order moment tensors is sqrt(p/n) wedge 1, while low-degree evidence shows detection of vanishing cumulants is hard for n much less than p to the d/2, creating a reverse detection-estimation gap.
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Mild Over-Parameterization Benefits Asymmetric Tensor PCA
A three-phase alternating-update method for asymmetric tensor PCA achieves d to the power of k-minus-2 sample complexity with d-squared memory and improves when signal vectors align.
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A functional tensor model for dynamic multilayer networks with common invariant subspaces and the RKHS estimation
A functional tensor model with common invariant subspaces and RKHS-based estimation is introduced for dynamic multilayer networks to handle shared structures, temporal smoothness, and layer heterogeneity.