Upper Bound of Real Log Canonical Threshold of Tensor Decomposition and its Application to Bayesian Inference
This work addresses the mathematical underpinnings of tensor decomposition for data analysis, providing theoretical insights into Bayesian inference, but it is incremental as it focuses on bounding an existing threshold.
The authors derived an upper bound for the real log canonical threshold (RLCT) of tensor decomposition using algebraic geometry, enabling theoretical calculation of Bayesian generalization error, with numerical experiments to explore its mathematical properties.
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.