In analyzing rs-fMRI, blind source separation has been studied extensively and various machine-learning techniques have been proposed in the literature. However, to our best knowledge, most of the existing methods do not explicitly separate noise components that naturally corrupt the observed BOLD signals, thus hindering from the understanding of underlying functional mechanisms in a human brain. In this paper, we formulate the problem of latent source separation in a probabilistic manner, where we explicitly separate the observed signals into a true source signal and a noise component. As for the inference of the latent source distribution with respect to an input regional mean signal, we use a stochastic variational Bayesian inference and implement it in a neural network framework. Further, in order for identification of a subject with early mild cognitive impairment (eMCI) rs-fMRI, we also propose to use the relations of the inferred source signals as features, i.e., potential imaging-biomarkers. We presented the validity of the proposed methods by conducting experiments on the publicly available ADNI2 dataset and comparing with the existing methods.