Collaborative Research: Nonparametric Bayesian Aggregation for Massive Data

现代海量数据呈现出海量增长、高度异构性的特点。例如互联网搜索、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合并到贝叶斯分层模型中。此外，通过贝叶斯计算可以很容易地进行不确定性量化。然而，由于存储和计算瓶颈，传统的在单机上实现的贝叶斯计算不再适用于现代海量数据。在这个项目中，基于一种称为分而治之的标准并行计算策略，开发了一套具有理论依据的非参数贝叶斯聚集过程。这项研究将大大提高贝叶斯工具和软件用于分析海量数据的可用性。该项目的教育计划将以研究生咨询和开设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。其次，PI将开发具有理论保证的非参数贝叶斯聚合过程，这对于以并行方式处理海量数据特别有用。第三，PI将为非参数贝叶斯模型开发一种高效的并行马尔可夫链蒙特卡罗(MCMC)算法，该算法的性能将与传统的MCMC算法相当，而计算量要小得多。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。PIS最近获得的光滑样条推理结果将被用作实现上述目标的有希望的工具。

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due to storage and computational bottlenecks, traditional Bayesian computation implemented in a single machine is no longer applicable to modern massive data.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