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Tensor Bernstein concentration inequalities with an application to sample estimators for high-order moments |
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| Authors: | Ziyan LUO Liqun QI Philippe L. TOINT |
| Affiliation: | 1. Department of Applied Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, China2. Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou 310018, China3. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China4. Namur Center for Complex Systems (naXys), University of Namur, 61, rue de Bruxelles, B-5000 Namur, Belgium |
| Abstract: | This paper develops the Bernstein tensor concentration inequality for random tensors of general order, based on the use of Einstein products for tensors. This establishes a strong link between these and matrices, which in turn allows exploitation of existing results for the latter. An interesting application to sample estimators of high-order moments is presented as an illustration. |
| Keywords: | Random tensors concentration inequality Einstein products sub-sampling computational statistics |
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