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首页> 外文期刊>Journal of machine learning research >Scaling up Data Augmentation MCMC via Calibration
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Scaling up Data Augmentation MCMC via Calibration

机译：通过校准缩放数据增强MCMC

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摘要

There has been considerable interest in making Bayesian inference more scalable. In big data settings, most of the focus has been on reducing the computing time per iteration rather than reducing the number of iterations needed in Markov chain Monte Carlo (MCMC). This article considers data augmentation MCMC (DA-MCMC), a widely used technique. DA-MCMC samples tend to become highly autocorrelated in large samples, due to a mis-calibration problem in which conditional posterior distributions given augmented data are too concentrated. This makes it necessary to collect very long MCMC paths to obtain acceptably low MC error. To combat this inefficiency, we propose a family of calibrated data augmentation algorithms, which appropriately adjust the variance of conditional posterior distributions. A Metropolis-Hastings step is used to eliminate bias in the stationary distribution of the resulting sampler. Compared to existing alternatives, this approach can dramatically reduce MC error by reducing autocorrelation and increasing the effective number of DA-MCMC samples per unit of computing time. The approach is simple and applicable to a broad variety of existing data augmentation algorithms. We focus on three popular generalized linear models: probit, logistic and Poisson log-linear. Dramatic gains in computational efficiency are shown in applications.
机译：使贝叶斯推理更加可扩展，有相当兴趣。在大数据设置中，大多数焦点都在降低每个迭代的计算时间，而不是减少马尔可夫链蒙特卡罗（MCMC）所需的迭代次数。本文考虑了数据增强MCMC（DA-MCMC），是一种广泛使用的技术。 DA-MCMC样本在大型样品中倾向于在大型样品中变得高度自相关，因为在给定的增强数据的条件后部分布太集中了。这使得必须收集非常长的MCMC路径以获得可接受的低MC错误。为了解决这种低效率，我们提出了一个校准的数据增强算法系列，适当地调整条件后分布的方差。 Metropolis-Hastings步骤用于消除所产生的采样器的固定分布中的偏置。与现有替代方案相比，这种方法可以通过减少自相关并增加每单位计算时间的DA-MCMC样本的有效数量来显着降低MC误差。该方法简单且适用于广泛的现有数据增强算法。我们专注于三个流行的广义线性模型：探测，逻辑和泊松日志线性。在应用中显示了计算效率的巨大收益。

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