权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Accelerating Bayesian Dimension Reduction for Dynamic Network Data with Many Observations

通过大量观察加速动态网络数据的贝叶斯降维

基本信息

批准号：
2152774
负责人：
Andrew Holbrook
金额：
$ 30万
依托单位：
University of California-Los Angeles
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-07-01 至 2025-06-30
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2152774&HistoricalAwards=false
关键词：
Accelerating Bayesian Dimension Reduction Dynamic

项目摘要

Global viral epidemics produce vast amounts of high-dimensional spatiotemporal data. Scientists, businesses, governments and independent organizations want to learn from this data so they can understand basic biological mechanisms, invest capital, allocate aid and design coherent policy in a changing world. Analyzing spatial associations within viral contagion is, unsurprisingly, an area of immense scientific interest, but the task requires accounting for the dynamic and multiscale transportation networks that shape the global economy. This project seeks to advance knowledge of statistical inference from stochastic process models in the context of massive amounts of dynamic and network-indexed data. The proposed research ideas will avoid costly direct representations of network structure and instead use Bayesian dimension reduction to probabilistically map network dynamics to a continuous domain. The project combines theoretical and methodological developments in scalable Bayesian dimension reduction; develops efficient algorithms into open-source, high performance computing (HPC) software; and applies them to the high-impact analysis of viruses including, but not limited to, SARS-CoV-2. The project will emphasize the combination of rigorous statistical methodology with parallel computing techniques available to any scientist with moderate resources.The project will combine theory, methods and applications in advancing knowledge of statistical inference for network-indexed processes. Bayesian multidimensional scaling (BMDS) stands as an established tool for probabilistic dimension reduction of network data but the method's quadratic computational complexity prohibits big data application. The project will extend BMDS to the analysis of millions of data points using a multipronged approach. From a theoretical standpoint, the investigators will show that the classical BMDS model is strictly equivalent to a modified BMDS model with sparse couplings between observations. This 'free lunch' result will amount to a linear reduction in the computational complexity of the classical algorithm, but its use will require an upper bound on the rank of the traditional BMDS distance matrix. A jointly methodological and theoretical investigation will develop a cutting-edge rank estimation procedure for Euclidean distance matrices (EDM) and derive non-asymptotic and asymptotic bounds for the rank estimation error and its impact on the modified BMDS posterior. Bayesian inference with the developed sparse BMDS (S-BMDS) will amount to simulating a massive N-body problem with sparse pairwise couplings. A primary methodological investigation will develop fast parallel algorithms for computing (1) the S-BMDS likelihood and gradient, and (2) the EDM rank in ways that efficiently use multi-core and vectorized central processing units (CPU) and multiple graphics processing units (GPU). The investigators will then allow trends in Google mobility data to inform effective distances between viruses and use our developed machinery to model the spread of, e.g., SARS-CoV-2 through global mobility space. The project also includes an expansive plan for educational, outreach and mentoring activities and will actively disseminate the research findings in a form of open-source HPC software.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

全球病毒流行产生了大量高维时空数据。科学家、企业、政府和独立组织希望从这些数据中学习，这样他们就可以了解基本的生物机制，投资资本，分配援助，并在不断变化的世界中设计连贯的政策。毫无疑问，分析病毒传染的空间关联是一个巨大的科学兴趣领域，但这项任务需要考虑塑造全球经济的动态和多尺度交通网络。该项目旨在在大量动态和网络索引数据的背景下推进随机过程模型的统计推断知识。提出的研究思路将避免昂贵的网络结构的直接表示，而是使用贝叶斯降维将网络动态概率映射到连续域。该项目结合了可扩展贝叶斯降维的理论和方法发展；将高效算法开发成开源、高性能计算（HPC）软件；并将其应用于病毒的高影响分析，包括但不限于SARS-CoV-2。该项目将强调将严谨的统计方法与任何拥有中等资源的科学家都可以使用的并行计算技术相结合。该项目将结合理论、方法和应用来推进网络索引过程的统计推断知识。贝叶斯多维尺度（BMDS）是一种成熟的网络数据概率降维工具，但该方法的二次计算复杂度阻碍了大数据的应用。该项目将利用多管齐下的方法将BMDS扩展到对数百万个数据点的分析。从理论的角度来看，研究人员将证明经典BMDS模型严格等效于观测之间具有稀疏耦合的修正BMDS模型。这种“免费午餐”的结果将相当于经典算法的计算复杂性的线性降低，但它的使用将需要传统BMDS距离矩阵的秩的上界。一个联合的方法和理论研究将开发一个先进的欧几里得距离矩阵（EDM）的秩估计程序，并推导秩估计误差的非渐近和渐近界及其对改进BMDS后验的影响。利用已开发的稀疏BMDS （S-BMDS）进行贝叶斯推理将相当于模拟具有稀疏成对耦合的大量n体问题。一项主要的方法研究将开发用于计算(1)S-BMDS似然和梯度的快速并行算法，以及(2)以有效使用多核和矢量化中央处理单元（CPU）和多个图形处理单元（GPU）的方式计算EDM秩。然后，研究人员将利用谷歌移动数据的趋势来了解病毒之间的有效距离，并使用我们开发的机器来模拟SARS-CoV-2通过全球移动空间的传播。该项目还包括一项广泛的教育、推广和指导活动计划，并将以开源HPC软件的形式积极传播研究成果。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。