You are presented with multiple paper abstracts, alongside the associated literature review and chapter titles. Given the provided information, you are going to do a literature review. Please generate a coherent literature review that synthesizes the content, draws connections between different works, highlights major findings, and identifies any gaps in the existing research.

Literature Review Title: Survey on Probabilistic Models of Low-Rank Matrix Factorizations 
Chapter Title:  Probabilistic Matrix Factorization 
1. Abstract of Cited Paper (BIB001):  The variational Bayesian (VB) approximation is known to be a promising approach to Bayesian estimation, when the rigorous calculation of the Bayes posterior is intractable. The VB approximation has been successfully applied to matrix factorization (MF), offering automatic dimensionality selection for principal component analysis. Generally, finding the VB solution is a nonconvex problem, and most methods rely on a local search algorithm derived through a standard procedure for the VB approximation. In this paper, we show that a better option is available for fully-observed VBMF--the global solution can be analytically computed. More specifically, the global solution is a reweighted SVD of the observed matrix, and each weight can be obtained by solving a quartic equation with its coefficients being functions of the observed singular value. We further show that the global optimal solution of empirical VBMF (where hyperparameters are also learned from data) can also be analytically computed. We illustrate the usefulness of our results through experiments in multi-variate analysis.

Literature Review:
We still consider Gaussian noise corruptions, that is, E ij ∼ N (0, σ 2 ). Furthermore, the zero-mean spherical Gaussian priors are respectively imposed on each row of W and each column of Z: Probabilistic matrix factorization (PMF) BIB001 regards both σ 2 w and σ 2 z as two deterministic parameters. The point estimations of W, Z can be obtained by maximizing the posterior distribution with the following form: If the priors are respectively placed on σ 2 w and σ 2 z , we can obtain the generalized model of probabilistic matrix factorization BIB001 . In this case, the likelihood function is derived as By maximizing the above posterior distribution, we can obtain the point estimations of parameters {W, Z} and hyperparameters σ 2 w , σ 2 z . Furthermore, two derivatives of PMF are also presented, i.e., PMF with a adaptive prior and PMF with constraining user-specific feature vectors. In BIB002 , a fully-observed variational Bayesian matrix factorization, an extension of PMF, was discussed. Meanwhile, it is shown that this new probabilistic matrix factorization can weaken the decomposability assumption and obtain the exact global analytic solution for rectangular cases.