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 family. Borrowing ideas from the classic boosting framework, recent approaches attempt to \emph{boost} VI by replacing the selection of a single density with a greedily 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.

本文提出了一种改进算法，基于强化版Variational Inference方法，用于更有效地近似概率密度，以此实现贝叶斯统计中重要的求解任务，提出的改进方法叫做Boosting VI。通过对算法的理论分析，证明了算法的收敛性和可行性，并且经过实验验证，该算法在实际应用中能够取得不错的效果。

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