Frameworks for Generic Robust Inference, Mismeasured Spatial and Network Data, and Nonlinear Dimension Reduction

这项研究项目将进行三个子项目，以改进现有的统计推断方法。需要更普遍适用、易于使用、基于模拟的统计推断方法，这些方法利用机器学习和其他先进数据处理技术的可用性。该项目将开发更广泛适用的基于模拟的推理方法。它将在基于空间或网络数据的模型中实现测量误差稳健推理。最后，该项目将提高非线性降维技术的可扩展性。在该项目下开发的基于模拟的统计推断方法将对整个数据科学产生重大影响。研究工作越来越依赖于复杂的数据分析方法，而传统的模拟方法无法提供可靠的推断。社会、医学和自然科学的研究越来越多地利用空间或网络数据以及高维数据的广泛可用性。这些领域将受到将要开发的方法的重大影响。研究生将在拟议方法的开发和实施中发挥重要作用。这个项目将通过使用广泛的新概念来推动现有推理方法的边界。研究人员将使用超级抽样的思想，即产生一个比数据集本身更大的扩大样本，并对其进行优化，以代表真实总体。这项研究将利用空间或网络数据中的相邻数据点来分离真实信号和噪声。该项目将基于观察到的样本或子集的现有重抽样方法的适用范围扩大到精心构建的大于样本的假设总体。该项目还将解决空间或网络环境中存在的测量误差问题，方法是将相邻数据点视为对感兴趣的真实基础变量的重复测量。这些测量不符合基于统计独立误差的经典框架，因此需要专门的技术。最后，将要使用的非线性降维技术将以新的方式融合最优传输、最大熵和基于模拟的估计的概念。降维技术在金融、心理学、神经学、数据压缩、信息检索和处理以及机器学习等领域都有广泛的应用。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This research project will conduct three sub-projects to improve upon existing statistical inference methods. There is a need for more generally applicable easy-to-use simulation-based statistical inference methods that exploit the availability of machine learning and other advanced data processing techniques. This project will develop more broadly applicable simulation-based inference methods. It will enable measurement-error robust inference in models based on spatial or network data. Finally, the project will improve the scalability of nonlinear dimension-reduction techniques. The simulation-based statistical inference methods developed under this project will have significant impact on data science in general. Research efforts increasingly rely on sophisticated data analysis methods where traditional simulation methods fail to provide reliable inference. Studies in the social, medical, and natural sciences increasingly are leveraging the broad availability of spatial or network data as well as high-dimensional data. These fields will be significantly impacted by the methods to be developed. Graduate students will play an important role in the development and implementation of the proposed methods.This project will push the boundary of existing inferential methods via the use of a broad range of novel concepts. The investigator will use the idea of super-sampling, in which an augmented sample, larger than the dataset itself, is generated and optimized to represent the true population. The research will exploit the idea of using neighboring data points in spatial or network data to disentangle the true signal from noise. The project extends that domain of applicability of existing resampling methods that are based on the observed sample or subsets to carefully constructed hypothetical populations larger than the sample. The project also will address the presence of measurement error in spatial or network contexts by viewing neighboring data points as repeated measurements of the true underlying variables of interest. These measurements do not conform to classical frameworks based on statistically independent errors and thus demand dedicated techniques. Finally, the nonlinear dimension-reduction techniques to be used will merge the concepts of optimal transport, entropy maximization, and simulation-based estimation in novel ways. Dimension reduction techniques have applications in fields as diverse as finance, psychology, neurology, data compression, information retrieval and processing, and machine learning.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.