Upper Bound of Real Log Canonical Threshold of Tensor Decomposition and its Application to Bayesian Inference
Machine Learning
2023-04-04 v2 Statistics Theory
Machine Learning
Statistics Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2303.05731,
title = {Upper Bound of Real Log Canonical Threshold of Tensor Decomposition and its Application to Bayesian Inference},
author = {Naoki Yoshida and Sumio Watanabe},
journal= {arXiv preprint arXiv:2303.05731},
year = {2023}
}