The Zig-Zag process and super-efficient sampling for Bayesian analysis of big data
Zig-Zag 过程与大数据贝叶斯分析的超高效抽样AI 解读 ↓
← 返回论文列表与筛选
阅读说明
本页整理公开书目信息，不生成学术质量评分。AI 解读根据题名及所注明的摘要或原文片段生成，未完成全文核验，可能有误；具体假设、证明与结论请核对原文。摘要保留来源文本，未经模型改写。
DOI 首次登记不等于接收或发表日期。部分更正、评论等条目没有独立摘要；缺少可靠材料时保留待补状态。
引用量采用 OpenAlex 单条关联记录，不合计多个记录；关联记录可能包含正式发表版本，不等于此版本单独引用。缺失不视为零，引用指标不代表论文质量。
关注作者按书目中的完整姓名匹配，同名和姓名变体需人工辨别。相关论文先按共享细分方向和具体方法排列，再参考通用方法与发表日期。
分类依据与纠错
AI 根据所提供的论文材料归类：摘要研究大数据贝叶斯通用抽样算法，未指定所列经济计量细分方向。
反馈分类问题
正在核对关联版本…
代码、数据与补充材料
正在核对对应版本的资源…
Zig-Zag 过程与大数据贝叶斯分析的超高效抽样
- 研究问题
- 如何减少大数据贝叶斯抽样中反复计算全样本似然的负担，同时保持目标后验，并使预处理后的抽样成本弱化对数据规模的依赖？
- 方法与思路
- 作者采用连续时间、分段确定且非可逆的 Zig-Zag 过程，结合子抽样与控制变量，研究无离散化误差模拟及遍历条件。
- 材料陈述的贡献
- 摘要称子抽样过程仍以后验为平稳分布；在结合控制变量及预处理的设定下，可使近独立样本的后续成本不依赖数据规模。
- 阅读关注点
- 应核对事件模拟、无偏估计和控制变量的构造、遍历条件，以及规模无关成本的成立条件、预处理代价和独立性度量。
- 阅读边界
- 仅据版本未注明的索引摘要；超高效结论的具体条件未说明，成本陈述须计及预处理，平稳分布正确也不代表有限运行已收敛。
原文摘要
Standard MCMC methods can scale poorly to big data settings due to the need to evaluate the likelihood at each iteration. There have been a number of approximate MCMC algorithms that use sub-sampling ideas to reduce this computational burden, but with the drawback that these algorithms no longer target the true posterior distribution. We introduce a new family of Monte Carlo methods based upon a multidimensional version of the Zig-Zag process of [Ann. Appl. Probab. 27 (2017) 846–882], a continuous-time piecewise deterministic Markov process. While traditional MCMC methods are reversible by construction (a property which is known to inhibit rapid convergence) the Zig-Zag process offers a flexible nonreversible alternative which we observe to often have favourable convergence properties. We show how the Zig-Zag process can be simulated without discretisation error, and give conditions for the process to be ergodic. Most importantly, we introduce a sub-sampling version of the Zig-Zag process that is an example of an exact approximate scheme, that is, the resulting approximate process still has the posterior as its stationary distribution. Furthermore, if we use a control-variate idea to reduce the variance of our unbiased estimator, then the Zig-Zag process can be super-efficient: after an initial preprocessing step, essentially independent samples from the posterior distribution are obtained at a computational cost which does not depend on the size of the data.