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Upper Bound of Real Log Canonical Threshold of Tensor Decomposition and its Application to Bayesian Inference

arXiv 2303.05731 ↗First posted 10 Mar 2023cs.LG math.ST stat.MLcited by 0

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Abstract (arXiv)

Tensor decomposition is now being used for data analysis, information compression, and knowledge recovery. However, the mathematical property of tensor decomposition is not yet fully clarified because it is one of singular learning machines. In this paper, we give the upper bound of its real log canonical threshold (RLCT) of the tensor decomposition by using an algebraic geometrical method and derive its Bayesian generalization error theoretically. We also give considerations about its mathematical property through numerical experiments.

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References · 3

  1. 2020The Exact Asymptotic Form of Bayesian Generalization Error in Latent Dirichlet Allocationcited by 14
  2. 2016Upper Bound of Bayesian Generalization Error in Non-negative Matrix Factorizationcited by 10
  3. 2022Asymptotic Behavior of Bayesian Generalization Error in Multinomial Mixturescited by 9

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