  In this paper, we propose a new message passing algorithm that utilizes
hybrid vector message passing (HVMP) to solve the generalized bilinear
factorization (GBF) problem. The proposed GBF-HVMP algorithm integrates
expectation propagation (EP) and variational message passing (VMP) via
variational free energy minimization, yielding tractable Gaussian messages.
Furthermore, GBF-HVMP enables vector/matrix variables rather than scalar ones
in message passing, resulting in a loop-free Bayesian network that improves
convergence. Numerical results show that GBF-HVMP significantly outperforms
state-of-the-art methods in terms of NMSE performance and computational
complexity.
