Accelerating Bayesian Dimension Reduction for Dynamic Network Data with Many Observations

全球病毒流行产生了海量的高维时空数据。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。不出所料，分析病毒传播中的空间关联是一个极具科学意义的领域，但这项任务需要考虑塑造全球经济的动态和多规模的交通网络。这个项目寻求在大量动态和网络索引数据的背景下，从随机过程模型中提高统计推断的知识。所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来将网络动态概率地映射到连续的域。该项目结合了可伸缩贝叶斯降维方面的理论和方法发展；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力分析，包括但不限于SARS-CoV-2。该项目将强调将严格的统计方法与任何拥有中等资源的科学家可用的并行计算技术相结合。该项目将结合理论、方法和应用，以提高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性阻碍了大数据的应用。该项目将使用多管齐下的方法将BMDS扩展到对数百万个数据点的分析。从理论上讲，研究人员将证明经典的BMDS模型严格等价于具有稀疏耦合的改进的BMDS模型。这种“免费午餐”的结果将使经典算法的计算复杂度线性降低，但它的使用将需要传统BMDS距离矩阵的秩上界。在方法论和理论研究的共同作用下，将发展欧氏距离矩阵(EDM)的前沿秩估计算法，并推导出秩估计量误差及其对修正的BMDS后验的影响的非渐近和渐近界。用发展的稀疏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规模N体问题。初步的方法论研究将开发快速并行算法，用于计算(1)S-BMDS似然和梯度，以及(2)有效使用多核和矢量化中央处理器和多图形处理器(GPU)的EDM排名。然后，调查人员将允许谷歌移动数据的趋势告知病毒之间的有效距离，并使用我们开发的机制来模拟SARS-CoV-2在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NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.