Variational Inference (VI) is an attractive alternative to Markov Chain Monte Carlo (MCMC) due to its computational efficiency in the case of large datasets and/or complex models with high-dimensional parameters. However, evaluating the accuracy of variational approximations remains a challenge. Existing methods characterize the quality of the whole variational distribution, which is almost always poor in realistic applications, even if specific posterior functionals such as the component-wise means or variances are accurate. Hence, these diagnostics are of practical value only in limited circumstances. To address this issue, we propose the TArgeted Diagnostic for Distribution Approximation Accuracy (TADDAA), which uses many short parallel MCMC chains to obtain lower bounds on the error of each posterior functional of interest. We also develop a reliability check for TADDAA to determine when the lower bounds should not be trusted. Numerical experiments validate the practical utility and computational efficiency of our approach on a range of synthetic distributions and real-data examples, including sparse logistic regression and Bayesian neural network models.

翻译：变分推断（VI）是马尔可夫链蒙特卡洛（MCMC）的一种有吸引力的替代方案，因其在处理大数据集和/或高维参数复杂模型时具有计算效率优势。然而，评估变分近似的精度仍是一项挑战。现有方法刻画的是整个变分分布的质量，而在实际应用中，即使诸如分量均值或方差等特定后验泛函是准确的，整个变分分布也几乎总是表现不佳。因此，这些诊断方法仅在有限场景下具有实用价值。为解决此问题，我们提出了分布近似精度针对性诊断方法（TADDAA），该方法利用多条短并行MCMC链获取每个感兴趣后验泛函误差的下界。我们还为TADDAA开发了一项可靠性检验，用于判定何时不应信任这些下界。数值实验在包括稀疏逻辑回归和贝叶斯神经网络模型在内的多种合成分布及真实数据示例上，验证了我们方法的实用性与计算效率。