Bayesian Allocation Model and Non-negative Matrix Factorization

We investigate a stochastic process called  “Bayesian Allocation Model” where tokens are allocated randomly to a tensor  and the probability for each index is specified by a graphical model. By integrating out some parameters of the model analytically, one obtains a Polya Urn Model, which enables one to calculate statistics about the model more efficiently by respecting the sparsity of the tensor.

By exploiting the relationship between this dynamic generative model and non-negative matrix/tensor factorization, we can look at NMF from another perspective.