We examine the \emph{submodular maximum coverage problem} (SMCP), which is related to a wide range of applications. We provide the first variational approximation for this problem based on the Nemhauser divergence, and show that it can be solved efficiently using variational optimization. The algorithm alternates between two steps: (1) an E step that estimates a variational parameter to maximize a parameterized \emph{modular} lower bound; and (2) an M step that updates the solution by solving the local approximate problem. We provide theoretical analysis on the performance of the proposed approach and its curvature-dependent approximate factor, and empirically evaluate it on a number of public data sets and several application tasks.

中文翻译：

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子模最大覆盖问题的变分优化

我们研究了\emph{子模最大覆盖问题}（SMCP），它与广泛的应用有关。我们基于 Nemhauser 散度为该问题提供了第一个变分近似，并表明可以使用变分优化有效地解决该问题。该算法在两个步骤之间交替：（1）E 步骤估计变分参数以最大化参数化 \emph{modular} 下界；(2) M 步，通过求解局部近似问题来更新解。我们对所提出的方法的性能及其曲率相关的近似因子进行了理论分析，并在许多公共数据集和几个应用任务上对其进行了实证评估。