Markov chain variational inference

Markov chain variational inference optimizes an initial parametric probability distribution ${\nu }_{\eta }$ by minimizing $\mathrm{KL}(K^t{\nu }_{\eta }\Vert \pi )$ after a fixed number of Markov kernel updates. The best initial probability distribution can depend on $t$; Kullback-Leibler divergence contraction does not imply that optimization commutes with applying the Markov kernel.