  Variational approximation has been widely used in large-scale Bayesian
inference recently, the simplest kind of which involves imposing a mean field
assumption to approximate complicated latent structures. Despite the
computational scalability of mean field, theoretical studies of its loss
function surface and the convergence behavior of iterative updates for
optimizing the loss are far from complete. In this paper, we focus on the
problem of community detection for a simple two-class Stochastic Blockmodel
(SBM) with equal class sizes. Using batch co-ordinate ascent (BCAVI) for
updates, we show different convergence behavior with respect to different
initializations. When the parameters are known or estimated within a reasonable
range and held fixed, we characterize conditions under which an initialization
can converge to the ground truth. On the other hand, when the parameters need
to be estimated iteratively, a random initialization will converge to an
uninformative local optimum.
