On the Accuracy of Hotelling-Type Tensor Deflation: A Random Tensor Analysis
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Leveraging on recent advances in random tensor theory, we consider in this paper a rank-r asymmetric spiked tensor model of the form ∑_i=1^r β_i A_i + W where β_i≥ 0 and the A_i's are rank-one tensors such that ⟨ A_i, A_j ⟩∈ [0, 1] for i≠ j, based on which we provide an asymptotic study of Hotelling-type tensor deflation in the large dimensional regime. Specifically, our analysis characterizes the singular values and alignments at each step of the deflation procedure, for asymptotically large tensor dimensions. This can be used to construct consistent estimators of different quantities involved in the underlying problem, such as the signal-to-noise ratios β_i or the alignments between the different signal components ⟨ A_i, A_j ⟩.
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