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The stochastic variational inference (SVI) paradigm, which combinesvariational inference, natural gradients, and stochastic updates, was recentlyproposed for large-scale data analysis in conjugate Bayesian models anddemonstrated to be effective in several problems. This paper studies a familyof Bayesian latent variable models with two levels of hidden variables butwithout any conjugacy requirements, making several contributions in thiscontext. The first is observing that SVI, with an improved structuredvariational approximation, is applicable under more general conditions thanpreviously thought with the only requirement being that the approximatingvariational distribution be in the same family as the prior. The resultingapproach, Monte Carlo Structured SVI (MC-SSVI), significantly extends the scopeof SVI, enabling large-scale learning in non-conjugate models. For models withlatent Gaussian variables we propose a hybrid algorithm, using both standardand natural gradients, which is shown to improve stability and convergence.Applications in mixed effects models, sparse Gaussian processes, probabilisticmatrix factorization and correlated topic models demonstrate the generality ofthe approach and the advantages of the proposed algorithms.

Monte Carlo Structured SVI for Two-Level Non-Conjugate Models