CAREER: Advances in Multi-scale Bayesian Inference and Learning on Massive Data

海量数据为我们进一步理解各种科学和社会现象提供了前所未有的机会。有了足够的数据和适当的统计工具，研究人员现在可以希望恢复数据中的结构，这些结构曾经被认为过于复杂，无法与传统的“小”数据相识别。 在海量数据中提取复杂的隐藏结构通常需要灵活的非参数方法;然而，有几个基本的挑战，使现有的非参数方法不切实际或不足。 这些挑战的核心是大数据分析中两个基本方面之间的冲突：（i）需要灵活的方法来捕获复杂的功能，以及（ii）与这种额外的灵活性相关的计算和统计成本。有效解决这一根本冲突需要新的非参数推理范式。该项目的长期研究目标是开发推理范式，包括理论，方法，算法和软件，用于有效解决这一根本冲突的非参数推理和学习。 该研究将导致统计工具的开发，以满足广泛领域的可扩展非参数数据分析的迫切需求，包括生物学，经济学，天体物理学，化学和信息技术。该项目将通过对本科生和研究生的教学和指导，以及对当地大学学生的宣传，解决研究与教育活动的整合问题。该项目将开发和研究一种特别有前途的范例，即多尺度分而治之，以解决灵活性和成本之间的根本冲突。 要解决的具体推理问题涵盖了广泛的非参数推理和学习目标，可以分为三个研究重点：（i）多个数据生成过程的联合非参数建模;（ii）表征随机变量/向量之间的依赖性;（iii）响应域集成监督学习。除了解决这些具体目标，拟议的研究将引入理论和计算设备，用于评估和提高多尺度分治方法的统计和计算效率。研究成果将包括对海量数据进行各种重要非参数推断任务的实用方法和算法，以及有效多尺度统计分析的一般指导原则。研究成果将通过出版物、演示文稿和开源软件传播给科学界和整个社会。该奖项反映了NSF的法定使命，并被认为值得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来支持。

Massive data present unprecedented opportunities for advancing our understanding of various scientific and social phenomena. With sufficient data and the appropriate statistical tools, researchers can now hope to recover structures in the data that were once deemed too intricate to identify with traditional "small" data. Extracting complex hidden structures in massive data often requires flexible nonparametric methods; however, there are several fundamental challenges that make existing nonparametric methods impractical or inadequate. At the core of these challenges is a conflict between two essential aspects in big data analysis: (i) the need for flexible methodology for capturing complex features and (ii) the cost, both computational and statistical, associated with this additional flexibility. Effective resolution of this fundamental conflict requires new paradigms of nonparametric inference. The long-term research objective of this project is to develop inference paradigms, including theory, methods, algorithms, and software, for nonparametric inference and learning that effectively resolve this fundamental conflict. The research will lead to the development of statistical tools that meet urgent needs for scalable nonparametric data analysis in a wide range of fields, including biology, economics, astrophysics, chemistry, and information technology. The project will address the integration of research with educational activities through teaching and mentoring of undergraduate and graduate students, and outreach to students from local colleges.This project will develop and investigate a particularly promising paradigm, multi-scale divide-and-conquer, to address the fundamental conflict between flexibility and cost. Specific inference problems to be addressed cover a wide range of nonparametric inference and learning objectives, and can be organized into three research thrusts: (i) joint nonparametric modeling of multiple data generative processes; (ii) characterizing dependency between random variables/vectors; and (iii) response-domain ensemble supervised learning. Beyond addressing these specific objectives, the proposed research will introduce theoretical and computational devices for evaluating and improving the statistical and computational efficiency of multi-scale divide-and-conquer methods in general. The output of the research will include practical methods and algorithms for carrying out a variety of important nonparametric inference tasks on massive data, as well as general guiding principles for effective multi-scale statistical analysis. The research output will be disseminated through publications, presentations, and open-source software to the scientific community, and society at large.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.