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

arXiv: https://arxiv.org/abs/2303.05731 · HTML: https://mlsanity.com/paper/2303.05731/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 22 references that are in the map.
- First posted on arXiv 10 Mar 2023.

## Builds on (most cited first, 3 of 3)

- [The Exact Asymptotic Form of Bayesian Generalization Error in Latent Dirichlet Allocation](https://mlsanity.com/paper/2008.01304/) (2020)
- [Upper Bound of Bayesian Generalization Error in Non-negative Matrix Factorization](https://mlsanity.com/paper/1612.04112/) (2016)
- [Asymptotic Behavior of Bayesian Generalization Error in Multinomial Mixtures](https://mlsanity.com/paper/2203.06884/) (2022)

## 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.