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Subsampling sequential Monte Carlo for static Bayesian models

机译：用于静态贝叶斯型号的子采样顺序蒙特卡罗

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摘要

We show how to speed up sequential Monte Carlo (SMC) for Bayesian inference in large data problems by data subsampling. SMC sequentially updates a cloud of particles through a sequence of distributions, beginning with a distribution that is easy to sample from such as the prior and ending with the posterior distribution. Each update of the particle cloud consists of three steps: reweighting, resampling, and moving. In the move step, each particle is moved using a Markov kernel; this is typically the most computationally expensive part, particularly when the dataset is large. It is crucial to have an efficient move step to ensure particle diversity. Our article makes two important contributions. First, in order to speed up the SMC computation, we use an approximately unbiased and efficient annealed likelihood estimator based on data subsampling. The subsampling approach is more memory efficient than the corresponding full data SMC, which is an advantage for parallel computation. Second, we use a Metropolis within Gibbs kernel with two conditional updates. A Hamiltonian Monte Carlo update makes distant moves for the model parameters, and a block pseudo-marginal proposal is used for the particles corresponding to the auxiliary variables for the data subsampling. We demonstrate both the usefulness and limitations of the methodology for estimating four generalized linear models and a generalized additive model with large datasets.
机译：我们展示了如何通过数据分配在大数据问题中加快呼叫蒙特卡罗（SMC）。 SMC通过一系列分布顺序更新粒子云，从易于采样的分布，诸如先前和结尾的分布，以后分布。粒子云的每次更新都包含三个步骤：重新传递，重采样和移动。在移动步骤中，使用马尔可夫内核移动每个粒子;这通常是最昂贵的昂贵的部分，特别是当数据集大时。有效的移动步骤至关重要，以确保粒子多样性。我们的文章提出了两个重要贡献。首先，为了加速SMC计算，我们使用基于数据分配的大致无偏见和有效的退火似然估计。子采样方法比相应的完整数据SMC更高，这是对并行计算的优势。其次，我们在Gibbs内核中使用了一个有两个条件更新的Metropolis。 Hamiltonian Monte Carlo更新使模型参数的远处移动，并且块伪边缘提案用于对应于数据限换的辅助变量的粒子。我们展示了用于估计四个广义线性模型和大型数据集的广义添加剂模型的方法的有用性和限制。

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  • 来源
    《Statistics and computing》 |2020年第6期|1741-1758|共18页
  • 作者

    Gunawan David; Dang Khue-Dung; Quiroz Matias; Kohn Robert; Tran Minh-Ngoc;

  • 作者单位

    Univ Wollongong Sch Math & Appl Stat Wollongong NSW Australia|ARC Ctr Excellence Math & Stat Frontiers ACEMS Parkville Vic Australia;

    Univ Technol Sydney Sch Math & Phys Sci Ultimo Australia|ARC Ctr Excellence Math & Stat Frontiers ACEMS Parkville Vic Australia;

    Univ Technol Sydney Sch Math & Phys Sci Ultimo Australia|ARC Ctr Excellence Math & Stat Frontiers ACEMS Parkville Vic Australia|Sveriges Riksbank Res Div Stockholm Sweden;

    Univ New South Wales Sch Econ UNSW Business Sch Kensington NSW Australia|ARC Ctr Excellence Math & Stat Frontiers ACEMS Parkville Vic Australia;

    ARC Ctr Excellence Math & Stat Frontiers ACEMS Parkville Vic Australia|Univ Sydney Discipline Business Analyt Sydney NSW Australia;

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  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Hamiltonian Monte Carlo; Large datasets; Likelihood annealing;

    机译：Hamiltonian Monte Carlo;大型数据集;可能性退火;

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