Fixed-form variational posterior approximation through stochastic linear regression

textabstractWe propose a general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribu- tion. Our method can be used to approximate any posterior distribution, provided that it is given in closed form up to the proportionality constant. The approxi- mation can be any distribution in the exponential family or any mixture of such distributions, which means that it can be made arbitrarily precise. Several exam- ples illustrate the speed and accuracy of our approximation method in practice