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Variational Inference (VI) is a method that approximates adifficult-to-compute posterior density using better behaved distributionalfamilies. VI is an alternative to the already well-studied Markov chain MonteCarlo (MCMC) method of approximating densities. With each algorithm, there areof course benefits and drawbacks; does there exist a combination of the twothat mitigates the flaws of both? We propose a method to combine CoordinateAscent Variational Inference (CAVI) with MCMC. This new methodology, termedHybrid CAVI, seeks to improve the sensitivity to initialization and convergenceproblems of CAVI by proposing an initialization using method of momentsestimates obtained from a short MCMC burn-in period. Unlike CAVI, Hybrid CAVIproves to also be effective when the posterior is not from a conditionallyconjugate exponential family.

Robust Coordinate Ascent Variational Inference with Markov chain Monte Carlo simulations