渐近精确数据增广：模型、性质和算法
Asymptotically exact data augmentation: models, properties and algorithms
摘要：
通过引入辅助变量的数据扩充已经成为一种普遍存在的技术，以提高收敛性能，简化实现或减少诸如马尔可夫链蒙特卡罗推理方法的计算时间。尽管如此，在保持初始目标概率分布的同时引入适当的辅助变量并提供计算上有效的推断不能以系统的方式进行。为了解决这些问题，本文研究了一个统一的框架，创造渐近精确数据增强（AXDA），其中包括完善的和最近的近似增强模型。从更广泛的角度来看，本文表明，AXDA模型可以受益于有趣的统计特性，并产生有效的推理算法。在非渐近设置中，所提出的近似的质量评估与几个理论结果。后者说明了标准的统计问题。补充材料，包括计算机代码，这篇论文可在网上。
英文摘要：
Data augmentation, by the introduction of auxiliary variables, has become an ubiquitous technique to improve convergence properties, simplify the implementation or reduce the computational time of inference methods such as Markov chain Monte Carlo ones. Nonetheless, introducing appropriate auxiliary variables while preserving the initial target probability distribution and offering a computationally efficient inference cannot be conducted in a systematic way. To deal with such issues, this paper studies a unified framework, coined asymptotically exact data augmentation (AXDA), which encompasses both well-established and more recent approximate augmented models. In a broader perspective, this paper shows that AXDA models can benefit from interesting statistical properties and yield efficient inference algorithms. In non-asymptotic settings, the quality of the proposed approximation is assessed with several theoretical results. The latter are illustrated on standard statistical problems. Supplementary materials including computer code for this paper are available online.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
