in machine learning, the cp-decomposition is the central ingredient in learning probabilistic latent variables models via the technique of moment-matching. for example, consider the multi-view model which is a probabilistic latent variable model. in this model, the generation of samples are posited as follows: there exists a hidden random variable that is not observed directly, given which, there are several conditionally independent random variables known as the different "views" of the hidden variable. for simplicity, assume there are three symmetrical views formula_157 of a formula_11-state categorical hidden variable formula_159. then the empirical third moment of this latent variable model can be written as: