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• W3042991564 abstract "We develop deterministic perturbation bounds for singular values and vectors of orthogonally decomposable tensors, in a spirit similar to classical results for matrices. Our bounds exhibit intriguing differences between matrices and higher-order tensors. Most notably, they indicate that for higher-order tensors perturbation affects each singular value/vector in isolation. In particular, its effect on a singular vector does not depend on the multiplicity of its corresponding singular value or its distance from other singular values. Our results can be readily applied and provide a unified treatment to many different problems involving higher-order orthogonally decomposable tensors. In particular, we illustrate the implications of our bounds through three connected yet seemingly different high dimensional data analysis tasks: tensor SVD, tensor regression and estimation of latent variable models, leading to new insights in each of these settings." @default.
• W3042991564 created "2020-07-23" @default.
• W3042991564 creator A5070196780 @default.
• W3042991564 creator A5076454131 @default.
• W3042991564 date "2020-07-17" @default.
• W3042991564 modified "2023-10-06" @default.
• W3042991564 title "Perturbation Bounds for Orthogonally Decomposable Tensors and Their Applications in High Dimensional Data Analysis." @default.
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• W3042991564 hasPublicationYear "2020" @default.
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