In SparseSCVB0, we obtain sparsity by substituting sparse Monte Carlo approximations γ (pseudo) ij for the original SCVB0 variational distributions γ ij .
the justification for this procedure, also used by (Mimno et al., 2012), is that the expected value of an average over one-hot samples from a distribution is equal to that distribution: the overall procedure is still a valid stochastic optimization algorithm.