Flexible Statistical Modelling for High Dimensional Data

科技创新使得海量高维数据在生物科学、医学研究、公共卫生、社会科学、电子商务、金融、气候研究等各个领域无处不在。在过去的十年中，统计学家已经开发了一套丰富的高维统计建模新工具。尽管有这些重要的进展，在高维数据分析中仍然有许多挑战和开放的问题需要处理。他们的解决方案需要创新的想法和技术来处理方法、计算和理论方面的挑战。本研究的目标是开发数学上可靠和计算上有效的方法来解决这些紧迫和重要的推理挑战。本研究由三个项目组成。第一个项目涉及高维m估计中的测量误差。PI将研究一种新的统一凸方法来解决变量误差惩罚的m回归，包括Huber回归，逻辑回归，分位数回归和支持向量机。在第二个项目中，PI将建立一个名为复合m估计的新推理工具，并演示其在高维学习中的应用。在第三个项目中，PI将研究一种灵活的异质性追求方法，以理解高维数据中的异质性效应。将创建软件包，使其他研究人员和实践者可以很容易地使用新方法。该奖项反映了美国国家科学基金会的法定使命，并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，被认为值得支持。

Scientific and technology innovations have made massive high-dimensional data ubiquitous in various fields, such as biological science, medical studies, public health, social sciences, e-commerce, finance, climate studies, and so on. During the past decade statisticians have developed a rich collection of new tools for high-dimensional statistical modeling. Despite these important advances, there are still many challenges and open problems to be dealt with in high-dimensional data analysis. Their solutions require innovative ideas and techniques to handle the methodological, computational and theoretical challenges. The goal of this research is to develop mathematically solid and computationally efficient methods to address these pressing and important inferential challenges. This research consists of three projects. The first project concerns measurement errors in high-dimensional M-estimation. The PI will study a new unified convex approach to solve the error-in-variables penalized M-regression including Huber regression, logistic regression, quantile regression, and the support vector machine. In the second project the PI will establish a new inference tool named composite M-estimation and demonstrate its applications in high-dimensional learning. In the third project the PI will study a flexible heterogeneity pursuit method for understanding the heterogeneity effects in high-dimensional data. Software packages will be created to make the new methods readily available to other researchers and practitioners.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.