CAREER: Locally Adaptive Nonparametric Estimation for the Modern Age - New Insights, Extensions, and Inference Tools

非参数建模-粗略地说，这意味着对平滑趋势进行灵活的建模，而不需要对其形式或形状做出具体假设-在流行病学、天体物理学、金融和人工智能等许多领域得到了广泛的应用。这也是一个适合现代统计学发展的成熟领域，因为在某种意义上，非参数模型在“大数据”时代更具吸引力，因为正是在数据丰富的环境中，这些模型的灵活性增加将开始在统计准确性方面显示出真正的回报。这项拟议的工作将开发非参数方法(及其附属软件)，这些方法将对数据科学家有用，他们将在上述领域以及许多其他领域对平滑、非线性趋势进行建模。一个具体的科学重点将是流感和登革热的预测。这样的预测将帮助政策制定者设计和实施针对这些疾病的更有效的对策。该建议提出了两个主要的教育培训思路，与所要追求的研究目标密切相关。第一个是一套关于非参数平滑的短片，旨在补充一门名为《数据分析的高级方法》的本科课程。它们将与交互式测验系统集成在一起，并将免费提供(在YouTube上)，以便班外的其他人也可以观看。第二个想法是为统计学和计算机科学的博士生设立一个统计计算培训小组。与传统的非参数方法相比，“局部自适应”非参数方法提供了更细粒度的灵活性，因为它们可以同时表示函数域不同部分的不同程度的光滑度。目前，局部自适应非参数方法并不经常用于大型现代数据集，这可能是因为它们的计算效率低下，并且在许多现代问题设置中通常无法使用局部自适应方法。提出的工作试图改变这一点，并推动现代局部自适应非参数估计的发展。研究的目的是：加深对现有单变量问题局部自适应方法的理论理解；有效地扩展这些方法，并将这些理论扩展到数据收集在高维和图形上的问题；并为所有这些局部自适应过程开发推理工具。具体的贡献将在理论(描述有关方法的基础的统计理论)和计算(描述大规模实施这些方法的实际算法)之间取得平衡。最后一个更实用的研究目标是使用拟议的方法来改进和扩展流感和登革热等重大流行病的预报系统。

Nonparametric modeling---which means, roughly, flexible modeling of smooth trends without specific assumptions about their form or shape---finds diverse applications in many areas such as epidemiology, astrophysics, finance, and artificial intelligence. It is also a field ripe for modern statistical development, since nonparametric models are in a sense even more appealing in the "big data" era, as it is precisely in data-rich settings that the increased flexibility of these models will begin to show real rewards in terms of statistical accuracy. The proposed work will develop nonparametric methods (and affiliated software) that will be useful to data scientists who model smooth, nonlinear trends in areas like those mentioned above, as well as many others. A specific scientific emphasis will be the forecasting of influenza and dengue fever. Such forecasts will help policy makers design and implement more effective countermeasures towards these diseases. The proposal puts forward two main ideas for educational training, closely related to the research aims to be pursued. The first is a set of short videos on nonparametric smoothing, intended as supplements to an undergraduate level course called Advanced Methods for Data Analysis. They will be integrated with an interactive quiz system, and will be made freely available (on YouTube) so that others outside the class may watch too. The second idea is a statistical computation training group, for PhD students from Statistics and Computer Science."Locally adaptive" nonparametric methods offer more fine-grained flexibility than traditional nonparametric methods, in that they can simultaneously represent different amounts of smoothness at different parts of the function domain. Currently, locally adaptive nonparametric methods are not often used in big, modern data sets, likely because of their computational inefficiency, and the general inavailability of locally adaptive methods in many modern problem settings. The proposed work seeks to change this, and to push the state of the art in modern locally adaptive nonparametric estimation. The research aims are to: deepen the theoretical understanding of existing locally adaptive methods for univariate problems; efficiently scale these methods and extend these theories to problems where data are collected in high dimensions and over graphs; and develop inferential tools for all of these locally adaptive procedures. The specific contributions will be balanced between the theoretical (statistical theories that describe the underpinnings of the methods in question) and computational (practical algorithms that describe implementation of these methods at scale) perspectives. A final more applied research aim is to use the proposed methods to improve and extend a forecasting system for major epidemics such as influenza and dengue fever.