As shown in Rubinstein and Kroese (2008) , the optimal choice of the proposal distribution is in fact the true posterior p(a|x), in which case the importance weight p(a,x) p(a|x) = p(x) is constant with respect to a. In<cite> Dyer et al. (2016)</cite> , the proposal distribution depends on x, i.e., q(a) q(a|x), and is computed with a separately-trained, discriminative model. This proposal choice is close to optimal, since in a fully supervised setting a is also observed and the discriminative model can be trained to approximate the true posterior well. We hypothesize that the performance of their importance sampler is dependent on this specific proposal distribution.