Validated Variational Inference via Practical Posterior Error Bounds
Validated Variational Inference via Practical Posterior Error Bounds
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发表时间：
2019-10
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通讯作者：
Jonathan Huggins;Mikolaj Kasprzak;Trevor Campbell;Tamara Broderick
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作者：
Jonathan Huggins;Mikolaj Kasprzak;Trevor Campbell;Tamara Broderick
变分推理已经成为一个越来越有吸引力的快速替代马尔可夫链蒙特卡罗方法的近似贝叶斯推理。然而，变分方法的广泛使用的一个主要障碍是缺乏事后的准确性措施，理论上是合理的和计算效率。在本文中，我们提供了严格的后验均值和不确定性估计的误差范围，所产生的全分布近似，在变分推理。我们的界限是广泛适用的，因为它们只需要近似和精确后验有多项式矩。我们的界限也计算效率变分推理，因为他们只需要标准值变分目标，简单的分析计算，和简单的蒙特卡罗估计。我们表明，我们的分析自然会导致一个新的和改进的工作流程验证变分推理。最后，我们证明了我们提出的工作流程和误差界上的鲁棒回归问题和一个实际数据的例子，广泛使用的多级层次模型的实用性。
Variational inference has become an increasingly attractive fast alternative to Markov chain Monte Carlo methods for approximate Bayesian inference. However, a major obstacle to the widespread use of variational methods is the lack of post-hoc accuracy measures that are both theoretically justified and computationally efficient. In this paper, we provide rigorous bounds on the error of posterior mean and uncertainty estimates that arise from full-distribution approximations, as in variational inference. Our bounds are widely applicable, as they require only that the approximating and exact posteriors have polynomial moments. Our bounds are also computationally efficient for variational inference because they require only standard values from variational objectives, straightforward analytic calculations, and simple Monte Carlo estimates. We show that our analysis naturally leads to a new and improved workflow for validated variational inference. Finally, we demonstrate the utility of our proposed workflow and error bounds on a robust regression problem and on a real-data example with a widely used multilevel hierarchical model.