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Divide and Couple: Using Monte Carlo Variational Objectives for Posterior Approximation
Justin Domke · Daniel Sheldon

Tue Dec 10 05:05 PM -- 05:10 PM (PST) @ West Ballroom C

Recent work in variational inference (VI) has used ideas from Monte Carlo estimation to obtain tighter lower bounds on the log-likelihood to be used as objectives for VI. However, there is not a systematic understanding of how optimizing different objectives relates to approximating the posterior distribution. Developing such a connection is important if the ideas are to be applied to inference—i.e., applications that require an approximate posterior and not just an approximation of the log-likelihood. Given a VI objective defined by a Monte Carlo estimator of the likelihood, we use a "divide and couple" procedure to identify augmented proposal and target distributions so that the gap between the VI objective and the log-likelihood is equal to the divergence between these distributions. Thus, after maximizing the VI objective, the augmented variational distribution may be used to approximate the posterior distribution.

Author Information

Justin Domke (University of Massachusetts, Amherst)
Daniel Sheldon (University of Massachusetts Amherst)

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