BIGDATA: F: Collaborative Research: Practical Analysis of Large-Scale Data with Lyme Disease Case Study

最近的技术和科学进步使人们能够获得大量不同类型的数据。如此丰富的信息应该会带来新的科学认识和突破。然而，这些数据的大规模性质带来了严重的复杂性，阻碍了传统的数据分析技术，导致许多领域的科学进步停滞不前。这个问题需要新颖的数学技术来有效地提取和分析信息。该项目将使用莱姆病数据（通过与LymeDisease.org的合作）作为设计和测试方法的激励例子，因为它是复杂的大规模数据的主要例子，对快速增长的社区具有非常重要的影响。因此，该项目的成果将迅速产生社会影响；例如，对LymeData的分析不仅可以进一步了解疾病本身，还可以使诊断更加准确和精确，为患者提供更加个性化和有效的治疗。此外，该提案将支持博士后、研究生和本科生的教育，并促进旨在增加代表性不足人群参与的外展工作。为了完成这一任务，除了本提案资助的活动外，pi还将利用现有的项目，如女性参与技术共享在线（WitsOn）项目、女性参与数据科学和数学研究合作研讨会（WiSDM）和洛杉矶MAPS 4学院，这些项目pi都已经积极参与，以招募代表性不足的人群并促进数学和技术科学。这个项目的基础研究将围绕三个主要目标展开，每个目标都针对大规模数据应用中出现的一个特别重要的挑战。第一个目标是设计适用于大数据的创新数据补全技术；这将涉及使用非随机（和非均匀）观测模式、自适应采样方案以及利用隐藏在观测中的附加结构的数据完成方法的设计和理论发展。该项目没有使用经典的（计算成本很高的）凸编程技术，而是将重点放在可以在推理任务期间实时运行的极其高效的简单求解器上。其次，该团队为推理任务提出了两种新的深度学习方法，这两种方法(i)计算效率极高，因此可以应用于大量数据集，以及（ii）实现现代深度学习方法的准确性优势，这些方法在最先进的方法基础上进行了改进。第三，该项目将开发关键的数据融合技术，允许以聚合方式分析来自各种来源的数据。最后，该团队建议将这三个数据分析任务结合在一个新的多阶段反馈设计中，其中来自数据完成、深度学习推理和融合的输出将作为这些机制的输入循环，以构建迭代和鲁棒推理框架。这些目标的进展将产生数据科学中新的数学框架，并提供将直接应用于大规模数据的技术，以实现高效和强大的数据分析。

Recent technological and scientific advances have allowed the acquisition of vast amounts of various types of data. Such an abundance of information should lead to new scientific understanding and breakthroughs. However, the large-scale nature of this data introduces serious complications that choke classical data analysis techniques, leading to a stagnation of scientific progress in many areas. This issue requires novel mathematical techniques in order to effectively extract and analyze the information. This project will use Lyme disease data (through a collaboration with LymeDisease.org) as a motivating example in the design and testing of the methods, as it serves as a prime example of complex large-scale data with very significant impact to a fast growing community. The results of this project will thus have swift societal impact; for example, analysis on the LymeData will not only further the understanding of the disease itself, but will also lead to more accurate and precise diagnoses, and more personalized and effective treatments for patients. In addition, this proposal will support the education of postdoctoral, graduate and undergraduate students, and facilitate outreach efforts aimed especially at increasing the participation of under-represented populations. To accomplish this task, in addition to the activities funded by this proposal, the PIs will utilize existing programs such as the Women In Technology Sharing Online (WitsOn) program, Women in Data Science and Mathematics Research Collaboration Workshop (WiSDM), and MAPS 4 College of Los Angeles, all in which the PIs are already actively involved, to recruit under-represented populations and to promote the mathematical and technical sciences.The fundamental research in this project will center around three main objectives, each addressing a particularly important challenge that arises in large-scale data applications. The first goal is to design innovative data completion techniques that are practical for big data; this will involve the design and theoretical development of data completion methods using non-random (and non-uniform) observation patterns, adaptive sampling schemes, and utilizing additional structures hidden in the observations. Rather than using classical (computationally expensive) convex programming techniques, the project will focus on extremely efficient simple solvers that can be run in real-time during an inference task. Secondly, the team proposes two novel deep learning approaches for inferential tasks that (i) are extremely computationally efficient and can thus be applied to massive datasets, and (ii) achieve the accuracy benefits of modern deep learning approaches, which improve upon state of the art methods. Third, the project will develop critical data fusion techniques that allow data from a wide variety of sources to be analyzed in an aggregated manner. Lastly, the team proposes to combine these three data analysis tasks in a novel multi-stage feedback design where outputs from data completion, deep learning inferences and fusion will be cycled back as inputs to these mechanisms for an iterative and robust inference framework. Progress on these goals will yield new mathematical frameworks in data science, and provide techniques that will be directly applied to large-scale data to allow efficient and powerful data analysis.