A variational Bayesian method for rectified factor analysis

Linear factor models with nonnegativity constraints have received a great deal of interest in a number of problem domains. In existing approaches, positivity has often been associated with sparsity. In this paper we argue that sparsity of the factors is not always a desirable option, but certainly a technical limitation of the currently existing solutions. We then reformulate the problem in order to relax the sparsity constraint while retaining positivity. A variational inference procedure is derived and this is contrasted to existing related approaches. Both i.i.d. and first-order AR variants of the proposed model are provided and these are experimentally demonstrated in a real-world astrophysical application.