Stochastic gradient Markov chain Monte Carlo algorithms have received much attention in Bayesian computing for big data problems, but they are only applicable to a small class of problems for which the parameter space has a fixed dimension and the log-posterior density is differentiable with respect to the parameters. This paper proposes an extended stochastic gradient Markov chain Monte Carlo algorithm which, by introducing appropriate latent variables, can be applied to more general large-scale Bayesian computing problems, such as those involving dimension jumping and missing data. Numerical studies show that the proposed algorithm is highly scalable and much more efficient than traditional Markov chain Monte Carlo algorithms.

中文翻译：

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扩展随机梯度马尔可夫链蒙特卡洛方法用于大规模贝叶斯变量选择

随机梯度马尔可夫链蒙特卡洛算法在贝叶斯计算中已经受到了大数据问题的广泛关注，但是它们仅适用于参数空间具有固定维数且对数后验密度相对可微的小类问题。参数。本文提出了一种扩展的随机梯度马尔可夫链蒙特卡洛算法，该算法通过引入适当的潜在变量，可以应用于更一般的大规模贝叶斯计算问题，例如涉及维数跳跃和数据丢失的问题。数值研究表明，与传统的马尔可夫链蒙特卡洛算法相比，该算法具有较高的可扩展性和效率。