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due to storage and computational bottlenecks, traditional Bayesian computation implemented in a single machine is no longer applicable to modern massive data.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.

现代海量数据呈现出数据量越来越大、异构性越来越高的特点。例子包括互联网搜索，社交网络，移动的设备，卫星，基因组学，医学扫描等贝叶斯方法是特别有用的，在这样的背景下，因为数据中的复杂结构可以自然地纳入贝叶斯分层模型。此外，不确定性量化可以通过贝叶斯计算轻松执行。然而，由于存储和计算瓶颈，在单机上实现的传统贝叶斯计算不再适用于现代海量数据。在这个项目中，一组非参数贝叶斯聚集过程的理论依据被称为分治的标准并行计算策略的基础上开发。这项研究将大大提高贝叶斯工具和软件的可用性，用于分析大量数据。该项目的教育计划将以研究生指导和提供专题课程的形式进行。该项目由三个主要部分组成。首先，PI将建立一般非参数后验分布的高斯近似，作为一般分布式贝叶斯算法的理论基础。第二，PI将开发一个非参数贝叶斯聚合过程，理论上的保证，是特别有用的，以并行方式处理大量数据。第三，PI将为非参数贝叶斯模型开发一种有效的并行马尔可夫链蒙特卡罗（MCMC）算法，该算法将与传统的MCMC一样，计算成本大大降低。这项研究将导致“分裂（分裂+渐近）理论”的出现，为贝叶斯实践提供理论指导。PI最近获得的平滑样条推理结果将被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