Adaptive higher-order spectral estimators
David Gerard, Peter Hoff
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Many applications involve estimation of a signal matrix from a noisy data matrix. In such cases, it has been observed that estimators that shrink or truncate the singular values of the data matrix perform well when the signal matrix has approximately low rank. In this article, we generalize this approach to the estimation of a tensor of parameters from noisy tensor data. We develop new classes of estimators that shri ...
nk or threshold the mode-specific singular values from the higher-order singular value decomposition. These classes of estimators are indexed by tuning parameters, which we adaptively choose from the data by minimizing Stein’s unbiased risk estimate. In particular, this procedure provides a way to estimate the multilinear rank of the underlying signal tensor. Using simulation studies under a variety of conditions, we show that our estimators perform well when the mean tensor has approximately low multilinear rank, and perform competitively when the signal tensor does not have approximately low multilinear rank. We illustrate the use of these methods in an application to multivariate relational data.
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Many applications involve estimation of a signal matrix from a noisy data matrix.
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Utility signals: depth 55/100, grounding 58/100, status medium.
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Research context
4
Citations
53
References
Tasks
Multilinear map, Estimator, Tensor (intrinsic definition), Singular value, Rank (graph theory), Matrix (chemical analysis), Singular value decomposition, SIGNAL (programming language)
Methods
Algorithm, Mathematical optimization
Domains
Mathematics, Applied mathematics, Artificial intelligence, Computational Mathematics
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