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Boosting Black Box Variational Inference
Francesco Locatello · Gideon Dresdner · Rajiv Khanna · Isabel Valera · Gunnar Ratsch

Thu Dec 06 07:45 AM -- 09:45 AM (PST) @ Room 210 #38

Approximating a probability density in a tractable manner is a central task in Bayesian statistics. Variational Inference (VI) is a popular technique that achieves tractability by choosing a relatively simple variational approximation. Borrowing ideas from the classic boosting framework, recent approaches attempt to \emph{boost} VI by replacing the selection of a single density with an iteratively constructed mixture of densities. In order to guarantee convergence, previous works impose stringent assumptions that require significant effort for practitioners. Specifically, they require a custom implementation of the greedy step (called the LMO) for every probabilistic model with respect to an unnatural variational family of truncated distributions. Our work fixes these issues with novel theoretical and algorithmic insights. On the theoretical side, we show that boosting VI satisfies a relaxed smoothness assumption which is sufficient for the convergence of the functional Frank-Wolfe (FW) algorithm. Furthermore, we rephrase the LMO problem and propose to maximize the Residual ELBO (RELBO) which replaces the standard ELBO optimization in VI. These theoretical enhancements allow for black box implementation of the boosting subroutine. Finally, we present a stopping criterion drawn from the duality gap in the classic FW analyses and exhaustive experiments to illustrate the usefulness of our theoretical and algorithmic contributions.

Author Information

Francesco Locatello (MPI Tübingen - ETH Zürich)
Gideon Dresdner (ETH Zürich)
Rajiv Khanna (University of Texas at Austin)
Isabel Valera (Max Planck Institute for Intelligent Systems)
Gunnar Ratsch (ETHZ)

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