Semiparametric Methods for Analysis of Complex Data

复杂数据分析的半参数方法

• 批准号: 2015569
• 负责人: Meng Li
• 金额: $ 10万
• 依托单位: William Marsh Rice University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-08-01 至 2023-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2015569&HistoricalAwards=false
• 关键词: Semiparametric; Methods; Analysis; Complex; Data

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.

在大数据时代，复杂数据在现代科学应用中自然产生。例如，计算和技术的进步使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巨大挑战，包括庞大的规模，复杂的依赖结构，以及对科学可解释性至关重要的各种形状约束。该项目将开发新的灵活的形状约束回归和高维分位数回归方法，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，以确保统计最优性和频率覆盖的同时置信度和可信带。将考虑使用功能和图像数据的几种制度，例如，均值回归，分位数回归和变量选择。该项目还将开发在形状约束下的非参数回归的新方法，包括局部稀疏性和未知函数的稳定点。该项目将通过开发一套理论上合理且计算效率高的半参数方法来丰富统计工具箱，以科普复杂的数据。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。

项目成果

On the Estimation of Derivatives Using Plug-in Kernel Ridge Regression Estimators

• 发表时间: 2020-06
• 作者: Zejian Liu;Meng Li

Efficient in-situ image and video compression through probabilistic image representation

通过概率图像表示实现高效的原位图像和视频压缩

• DOI: 10.1016/j.sigpro.2023.109268
• 发表时间: 2024
• 期刊: Signal Processing
• 影响因子: 4.4
• 作者: Liu, Rongjie;Li, Meng;Ma, Li
• 通讯作者: Ma, Li

Functional group bridge for simultaneous regression and support estimation

• DOI: 10.1111/biom.13684
• 发表时间: 2020-06
• 期刊: Biometrics
• 影响因子: 1.9
• 作者: Zhengjia Wang;J. Magnotti;M. Beauchamp;Meng Li

Inference in functional linear quantile regression

• DOI: 10.1016/j.jmva.2022.104985
• 发表时间: 2016-02
• 期刊: Journal of multivariate analysis
• 影响因子: 1.6
• 作者: M. Li;K. Wang;A. Maity;A. Staicu

Learning Asymmetric and Local Features in Multi-Dimensional Data Through Wavelets With Recursive Partitioning

• DOI: 10.1109/tpami.2021.3110403
• 发表时间: 2017-11
• 期刊: IEEE Transactions on Pattern Analysis and Machine Intelligence
• 影响因子: 23.6
• 作者: Meng Li;Li Ma