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

Tensor decomposition is widely used in data science and machine learning [1]. For instance, It plays the central roles in signal processing by contribution analysis [2], data compression by converting tensor data to matrix data [3], and data recovery by counting backwards from the matrices to the original tensor data [4]. In many cases, tensor decomposition itself is known to be NP-hard [5]. For this reason, tensor decomposition is often calculated approximately by Bayesian inference. However, its mathematical property is not yet completely clarified because it is one of the singular statistical models. In this paper, we derive its generalization performance in Bayesian inference. Tensor decomposition has mainly two types: Tucker decomposition and CP decomposition.