Semiparametric Methods for Analysis of Complex Data

大数据时代，复杂数据在现代科学应用中自然而然地出现。例如，计算和技术的进步使得高频功能数据和高分辨率图像的常规收集成为可能。科学家们正面临着来自数据的严峻挑战，包括大规模、复杂的依赖结构以及对科学解释性至关重要的各种形状限制。该项目将为形状约束回归和高维分位数回归开发新的灵活方法，以全面描述变量之间的依赖关系，重点是提供可扩展的实现和理论上有保证的推理。这些工具将解决紧迫的统计和计算挑战，从而在医学、神经科学、癌症相关研究和工业环境中得到广泛应用。该项目还将开发和分发开源软件，并为本科生和研究生提供研究机会。该项目将为高维分位数回归和形状约束回归开发新颖的半参数方法。 PI 将研究高维回归从联合迭代方案到两步分布式方案的范式转变。该策略允许利用并行计算，并与适当的不确定性传播相结合，以确保统计最优性以及同时置信度和可信带的频率覆盖。将考虑使用功能和图像数据的几种方案，例如均值回归、分位数回归和变量选择。该项目还将开发形状约束下非参数回归的新方法，包括局部稀疏性和未知函数的驻点。该项目将通过开发一套理论上合理且计算高效的半参数方法来丰富统计工具箱，以应对复杂的数据。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力优点和更广泛的影响审查标准进行评估，被认为值得支持。

In the era of big data, complex data naturally arise in modern scientific applications. For example, the advance in computation and technology has enabled the routine collection of high-frequency functional data and high-resolution images. Scientists are facing daunting challenges from the data, including the massive scale, intricate dependence structures, and various shape constraints that are vital for scientific interpretability. This project will develop new flexible methods for shape-constrained regression and high-dimensional quantile regression to comprehensively depict the dependence between variables, with a focus on providing scalable implementation and theoretically guaranteed inference. These tools will address pressing statistical and computational challenges, leading to broad applications in medicine, neuroscience, cancer-related studies, and industrial settings. The project will also develop and distribute open-source software and provide research opportunities for undergraduate and graduate students. The project will develop novel semiparametric methods for high-dimensional quantile regression and shape-constrained regression. The PI will investigate a paradigm shift in high-dimensional regression from a joint, iterative scheme to a two-step, distributed scheme. This strategy allows the utilization of parallel computation and is coupled with proper uncertainty propagation to ensure statistical optimality and frequentist coverage of simultaneous confidence and credible bands. Several regimes using functional and image data will be considered, for example, mean regression, quantile regression, and variable selection. The project will also develop new methods for nonparametric regression under shape constraints, including local sparsity and stationary points of unknown functions. The project will enrich the statistical toolbox to cope with complex data by developing a suite of semiparametric methods that are theoretically sound and computationally efficient.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.