TRIPODS: Towards a Unified Theory of Structure, Incompleteness & Uncertainty in Heterogeneous Graphs

该项目汇集了来自数学、统计学和计算机科学的研究人员，开发了应用于不确定和异构图和网络数据的数据科学的统一理论。大多数网络的实际应用涉及复杂的现象，如社会行为交互、生物和/或化学过程、数据中心等技术系统和智能城市的通信系统。这些数据是异构的，包括多种模式和多种尺度。至关重要的是，观测到的数据往往是不完整的，而且非常嘈杂。为了应对图和网络数据背景下的这些挑战，需要建立一个新的数据科学基础。同样，我们缺乏一个清晰的统一理论，使我们能够理解如何量化系统中由参与者之间关系的不确定性产生的不确定性。这是统计学家、数学家和计算机科学家之间跨学科合作的肥沃领域，对工业、学术界、政府和更广泛的社会产生了强大的影响。本项目围绕两个研究主题展开。在第一个主题中，pi将研究不确定网络数据的算法模型，特别是将亚线性算法与贝叶斯方法相结合的技术。第二个主题侧重于算法如何从数据不确定性中受益，在隐私，披露和对噪声的鲁棒性的背景下。在这两个主题中，技术进步将通过将不确定性的计算方法与不确定性的统计和数学方法相结合来实现。除了研究议程之外，该项目还涉及一个跨越学术界到工业界的数据科学能力的雄心勃勃的愿景。这一愿景的教育方面包括一系列主题研讨会和开发涵盖中学、本科和高级研究生材料的综合教育资源。该项目还涉及加州大学圣克鲁斯分校和硅谷公司之间的合作，将我们提出的理论和算法进步与实际应用结合起来，解决现实世界的问题和数据。此外，这些与工业伙伴的合作将导致专业化的劳动力发展。展望第二阶段，该项目旨在与该地区的行业合作伙伴和各种学术机构建立合作关系，以建立硅谷/大湾区数据科学基础研究所，该研究所可能位于加州大学圣克鲁斯分校硅谷圣克拉拉校区。该项目的资金来自CISE信息技术研究和MPS数学科学部。

This project brings together researchers from mathematics, statistics, and computer science to develop a unified theory of data science applied to uncertain and heterogeneous graph and network data. Most real-world applications of networks involve complex phenomena, such as socio-behavioral interactions, biological and/or chemical processes, technical systems like data centers, and communication systems for smart cities. These data are heterogeneous, including multiple modalities and multiple scales. Crucially, the data observed is often incomplete and very noisy. A new foundation for data science needs to be built in order to address these challenges in the context of graph and network data. Similarly, we lack a clear unified theory that allows us to understand how to quantify the uncertainty in the system that arises from the uncertainty in the relationships among its actors. This is a fertile area for transdisciplinary collaboration between statisticians, mathematicians, and computer scientists, with strong impacts on industry, academia, government and broader society. This project centers around two research themes. In the first theme, the PIs will investigate models of algorithms on uncertain network data, and specifically combine techniques from sub-linear algorithms with Bayesian methods. The second theme focuses on how algorithms can benefit from data uncertainty, in the context of privacy, disclosure, and robustness to noise. In both these themes, technical advances will be achieved by marrying computational approaches to uncertainty with statistical and mathematical approaches for uncertainty. In addition to the research agenda, the project involves an ambitious vision for data science capabilities spanning academia to industry. The education aspects of this vision include a series of themed workshops and the development of comprehensive educational resources spanning secondary, undergraduate and advanced graduate materials. The project also involves collaboration between UC Santa Cruz and Silicon Valley companies that will ground our proposed theoretical and algorithmic advances with practical applications to real-world problems and data. Furthermore, these collaborations with industrial partners will lead to specialized workforce development. Looking forward towards Phase II, the project aims to develop collaborations with industry partners and various academic institutions in the area to develop a Silicon Valley/Greater Bay Area Institute on Foundations of Data Science, potentially to be located at University of California Santa Cruz Silicon Valley campus in Santa Clara. Funds for the project come from CISE Information Technology Research and MPS Division of Mathematical Sciences.