Automatic differentiation variational inference (ADVI) offers fast and easy-to-use posterior approximation in multiple modern probabilistic programming languages. However, its stochastic optimizer lacks clear convergence criteria and requires tuning parameters. Moreover, ADVI inherits the poor posterior uncertainty estimates of mean-field variational Bayes (MFVB). We introduce ``deterministic ADVI'' (DADVI) to address these issues. DADVI replaces the intractable MFVB objective with a fixed Monte Carlo approximation, a technique known in the stochastic optimization literature as the ``sample average approximation'' (SAA). By optimizing an approximate but deterministic objective, DADVI can use off-the-shelf second-order optimization, and, unlike standard mean-field ADVI, is amenable to more accurate posterior linear response (LR) covariance estimates. In contrast to existing worst-case theory, we show that, on certain classes of common statistical problems, DADVI and the SAA can perform well with relatively few samples even in very high dimensions, though we also show that such favorable results cannot extend to variational approximations that are too expressive relative to mean-field ADVI. We show on a variety of real-world problems that DADVI reliably finds good solutions with default settings (unlike ADVI) and, together with LR covariances, is typically faster and more accurate than standard ADVI.

翻译：自动微分变分推断（ADVI）在多种现代概率编程语言中提供快速且易用的后验近似。然而，其随机优化器缺乏明确的收敛准则并需要调整参数。此外，ADVI继承了平均场变分贝叶斯（MFVB）后验不确定性估计较差的缺陷。我们提出“确定性ADVI”（DADVI）以解决这些问题。DADVI将难以处理的MFVB目标替换为固定蒙特卡罗近似，该技术随机优化文献中称为“样本平均近似”（SAA）。通过优化近似但确定性的目标，DADVI可直接使用现成的二阶优化方法，且与标准平均场ADVI不同，它适用于更精确的后验线性响应（LR）协方差估计。与现有最坏情况理论相反，我们证明：在若干常见统计问题类别中，即使在高维场景下，DADVI和SAA也能用相对较少的样本取得良好表现，尽管我们同时证明，当变分近似相对于平均场ADVI过度表达时，此类有利结果无法推广。我们在多种实际问题中表明，DADVI能在默认设置下可靠找到优质解（与ADVI不同），并且结合LR协方差后，通常比标准ADVI更快且更准确。