BAYESIAN EXTENSIONS TO ITAKURA-SAITO NMF

Bayesian NMF

The ML likelihood framework presented above inherently assumes W and H to be deterministic parameters with no prior information available. In this section we turn to a Bayesian setting where the parameters are given prior distributions p(W) and p(H), reflecting prior beliefs such as smoothness, sparsity, structure, etc. Bayesian inference revolves around the posterior distribution of the set of all unknown parameters: information about θ or subsets of θ is inferred from the data through manipulation of the posterior. As such, typical point estimates are the maximum a posteriori (MAP) estimate