Collaborative Research: Nonparametric Bayesian Aggregation for Massive Data

协作研究：海量数据的非参数贝叶斯聚合

• 批准号: 1712907
• 负责人: Guang Cheng
• 金额: $ 14万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-09-01 至 2020-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1712907&HistoricalAwards=false
• 关键词: Collaborative; Research; Nonparametric; Bayesian; Aggregation

Modern massive data appear in increasing volume and high heterogeneity. Examples include internet searches, social networks, mobile devices, satellites, genomics, medical scans, etc. Bayesian approaches are particularly useful in such context since the complex structures in the data can be naturally incorporated in Bayesian hierarchical models. Besides, uncertainty quantification can be easily executed through Bayesian computation. However, due to storage and computational bottlenecks, traditional Bayesian computation implemented in a single machine is no longer applicable to modern massive data. In this project, a set of nonparametric Bayesian aggregation procedures with theoretical justifications are developed based on a standard parallel computing strategy known as Divide-and-Conquer. This research will significantly enhance the availability of Bayesian tools and software for analyzing massive data. The educational plan of the project will be in the form of graduate student advising and offering of special topics courses. This project consists of three major components. First, the PIs will establish a Gaussian approximation of general nonparametric posterior distributions which serves as a theoretical foundation for general distributed Bayesian algorithms. Second, the PIs will develop a nonparametric Bayesian aggregation procedure with theoretical guarantees that is particularly useful to handle massive data in a parallel fashion. Third, the PIs will develop an efficient parallel Markov Chain Monte Carlo (MCMC) algorithm for nonparametric Bayesian models which will perform as well as traditional MCMC with substantially less computational costs. This research will lead to an emergence of "Splitotics (Split+Asymptotics) Theory" providing theoretical guidelines for Bayesian practices. The smoothing spline inference results recently obtained by the PIs will be used as a promising tool for achieving the above goals.

现代大规模数据的体积增加和高异质性。示例包括互联网搜索，社交网络，移动设备，卫星，基因组学，医学扫描等。贝叶斯方法在这种情况下特别有用，因为数据中的复杂结构可以自然地纳入贝叶斯层次结构模型中。此外，不确定性量化可以通过贝叶斯计算轻松执行。但是，由于存储和计算瓶颈，单台机器中实施的传统贝叶斯计算不再适用于现代大型数据。在这个项目中，一组具有理论理由的非参数贝叶斯聚合程序是基于标准的平行计算策略（称为分裂和串联的标准计算策略）开发的。这项研究将大大提高贝叶斯工具和软件的可用性，以分析大量数据。该项目的教育计划将以研究生的形式为特殊主题课程提供建议和提供。该项目由三个主要组成部分组成。首先，PI将建立一般非参数后分布的高斯近似，这是一般分布式贝叶斯算法的理论基础。其次，PIS将开发非参数贝叶斯聚合程序，并具有理论保证，这对于以并行方式处理大量数据特别有用。第三，PIS将开发出一种非参数贝叶斯模型的有效的平行马尔可夫链蒙特卡洛（MCMC）算法，该算法将与传统的MCMC相同，并且计算成本较小。这项研究将导致出现“分裂学（分裂+渐近学）理论”，从而为贝叶斯实践提供了理论指南。 PI最近获得的平滑样条推断结果将用作实现上述目标的有前途的工具。

项目成果

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• 发表时间: 2018
• 期刊: Advances in neural information processing systems
• 作者: Liu, M;Cheng, G.
• 通讯作者: Cheng, G.

High Dimensional Inference in Partially Linear Models

• DOI: 10.2139/ssrn.3015397
• 发表时间: 2017-08
• 期刊: Mathematics eJournal
• 作者: Ying Zhu;Zhuqing Yu;Guang Cheng

Gaussian approximation for high dimensional vector under physical dependence

• DOI: 10.3150/17-bej939
• 发表时间: 2018-11
• 期刊: Bernoulli
• 影响因子: 1.5
• 作者: Xianyang Zhang;Guang Cheng

Early Stopping for Nonparametric Testing

非参数测试的提前停止

• 发表时间: 2018
• 期刊: Proceedings of the 32nd International Conference on Neural Information Processing
• 作者: Liu, M.;Cheng, G.
• 通讯作者: Cheng, G.

Tensor Graphical Model: Non-Convex Optimization and Statistical Inference

• DOI: 10.1109/tpami.2019.2907679
• 发表时间: 2016-09
• 期刊: IEEE Transactions on Pattern Analysis and Machine Intelligence
• 影响因子: 23.6
• 作者: Xiang Lyu;W. Sun;Zhaoran Wang;Han Liu;Jian Yang;Guang Cheng