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Variational inference is computationally challenging in models that containboth conjugate and non-conjugate terms. Methods specifically designed forconjugate models, even though computationally efficient, find it difficult todeal with non-conjugate terms. On the other hand, stochastic-gradient methodscan handle the non-conjugate terms but they usually ignore the conjugatestructure of the model which might result in slow convergence. In this paper,we propose a new algorithm called Conjugate-computation Variational Inference(CVI) which brings the best of the two worlds together -- it uses conjugatecomputations for the conjugate terms and employs stochastic gradients for therest. We derive this algorithm by using a stochastic mirror-descent method inthe mean-parameter space, and then expressing each gradient step as avariational inference in a conjugate model. We demonstrate our algorithm'sapplicability to a large class of models and establish its convergence. Ourexperimental results show that our method converges much faster than themethods that ignore the conjugate structure of the model.

Conjugate-Computation Variational Inference : Converting Variational Inference in Non-Conjugate Models to Inferences in Conjugate Models