ATD: New Algorithms for Inference and Predictions on Large Geospatial Datasets

该项目的目标是准确建模、监测和预测大规模、公开可用的地理空间数据集。特别是，我们将专注于不同的对抗现象与空间和时间维度之间复杂的相互作用。2020年在现代历史上留下了一个重要的印记，毁灭性的COVID-19大流行影响了世界各地。考虑到不同的政府策略和不同地区的疫苗接种率，这就产生了具有有趣的时间动力学的大型时空数据集。从数据中了解这些时空趋势并准确预测未来可能是减轻传染病的关键。这种类型的时空数据也存在于许多其他重要的应用中。例如，执法机构面临的一个关键挑战是以高效和有效的方式从历史和即将到来的犯罪记录数据中学习，从而优化资源分配。时空数据的其他重要例子出现在理解环境变量、研究一段时间内的大脑图像和不同节点、理解交通流量以及在很长一段时间内检查卫星图像。尽管是特定于场所的应用，但该提案的吸引力在于建立一个全面和包容的框架，在这个框架中，现有的多元方法将被策划，以突出空间和时间如何相互作用。该项目将为研究生提供研究培训机会。该项目将侧重于以下方法学方面：i)估计合适的变系数模型，同时对系数进行适当的置信带，以帮助了解这些系数如何随时间和空间变化，然后，如果可行，选择更简单的这些系数随时间和空间的建模ii)识别与人类动力学相关的重要协变量，战略采用；其他外部干预措施以及它们如何影响这些变量随时间和空间的分布，最后iii)对未来的短期和长期前景提供准确而有力的预测。现有的时空数据文献要么假设了一个非常具体的模型，要么建立了不同时间戳的空间分布的比较框架，从而忽略了空间和时间之间可能存在的非线性和不可分的相互作用。本项目利用多元时间序列的一些最新发展，并将其扩展到时空场景来解决这种普遍性。由于地理空间数据非常大，因此该项目还利用了高维统计文献中最近取得的重大进展，并提出了可以包含非常普遍的时空依赖性的新方法。新方法将在广泛的时空数据集上进行测试，并有望获得关于这些复杂随机过程如何在空间和时间上传播的新见解。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。

The goal of this project is to accurately model, monitor and forecast large-scale, publicly available geo-spatial datasets. In particular, we will focus on different adversarial phenomena with complex interactions between space and time dimensions. The year 2020 has left a significant mark in modern history with the devastating COVID-19 pandemic that impacted every part of the world. This gave rise to large spatio-temporal datasets with interesting time-dynamics, given different government strategies and vaccination rates in different locations. Understanding these spatio-temporal trends from the data and accurately forecasting what the future holds could be a key in mitigating contagious diseases. This type of spatio-temporal data is present in many other important applications as well. For example, one key challenge for law enforcement agencies is to learn from both historical and incoming crime log data in an efficient and effective fashion so as to optimize resource allocation. Other significant examples of spatio-temporal data arise in understanding environmental variables, studying brain images and different nodes for a period of time, understanding traffic flow, and inspection of satellite image over a long horizon of time. Despite being specific to the application at places, the appeal of this proposal is to build a comprehensive and inclusive framework where existing multivariate methods will be curated to highlight how space and time interact with each other. The project will provide research training opportunities for graduate students. This project will focus on the following methodological aspects: i) Estimate suitable varying coefficient models with proper simultaneous confidence bands for the coefficients to help realize how these vary over time and space and then if plausible, choose simpler modeling of these coefficients over time and space ii) Identify important covariates related to human dynamics, strategic adoption, other external interventions and how they impact these variables spread over time and space and finally iii) Provide an accurate yet robust forecast for both short- and long-time horizon in the future. The existing literature on spatio-temporal data either assumes a very specific model or builds a comparative framework of the spatial distribution for different time-stamps and thus ignores a possible non-linear and non-separable interaction between space and time. This project uses some recent developments in multivariate time-series and extend them to a spatio-temporal scenario to address such generality. Since geo-spatial data are prohibitively large, the project also leverages the recent significant advances made in high-dimensional statistics literature and proposes new methods that can incorporate a very general space-time dependence. The new methods will be tested on a wide array of spatio-temporal datasets and are expected to derive new insights about how these complex stochastic processes are spread over space and time.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.