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.
Tensor moments of Gaussian mixture models: Theory and applications
2 Pith papers cite this work. Polarity classification is still indexing.
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Algorithm for low-rank decomposition of partially symmetric tensors via flattening orthogonalization and shifted power method with global convergence proof.
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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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Multi-subspace power method for decomposing partially symmetric tensors
Algorithm for low-rank decomposition of partially symmetric tensors via flattening orthogonalization and shifted power method with global convergence proof.