  The assumption that the values of model parameters are known or correctly
learned, i.e., the Nishimori condition, is one of the requirements for the
detectability analysis of the stochastic block model in statistical inference.
In practice, however, there is no example demonstrating that we can know the
model parameters beforehand, and there is no guarantee that the model
parameters can be learned accurately. In this study, we consider the
expectation--maximization (EM) algorithm with belief propagation (BP) and
derive its algorithmic detectability threshold. Our analysis is not restricted
to the community structure, but includes general modular structures. Because
the algorithm cannot always learn the planted model parameters correctly, the
algorithmic detectability threshold is qualitatively different from the one
with the Nishimori condition.
