For example, if f = Dir(α) It makes the marginal expectations Similarly we can represent up to the third moments: By assuming w ∼ Dir(α), we can fortunately attain closed form expressions of all three population moments only in terms of B and α, allowing the non-central second and third moments to be further represented by lower-order moments and α 0 (Anandkumar et al., 2012a).
once users construct the empirical moments given the training data and choose α 0 , tensor decomposition allows us to recover B and α up to some precision by matching the empirical moments to these population moments.