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Slow Kill for Big Data Learning

大数据学习的慢杀

基本信息

批准号：
2113599
负责人：
Yiyuan She
金额：
$ 17万
依托单位：
Florida State University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-09-01 至 2025-08-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2113599&HistoricalAwards=false
关键词：
Slow Kill Big Data Learning

项目摘要

Big-data applications typically involve large numbers of samples and features and are often contaminated with outliers, posing challenges for variable selection and parameter estimation. Fitting a sparse model with a prescribed cardinality is a common request in practice, but it is associated with solving a highly nonconvex and discrete problem. Using multiple starting points in such nonconvex optimization is common, but is often computationally prohibitive on big data; new cost-effective techniques are needed to alleviate the starting point requirement and ensure the best statistical accuracy. Moreover, how to adjust an arbitrarily given loss function to guard against gross outliers and achieve a high break-down point poses a major challenge for modern-day data analysis. The project will study innovative and efficient statistical methods and perform rigorous theoretical analysis to answer these questions. In this project, education is tightly coupled with research, consisting of course development, student mentoring, outreach, and recruiting underrepresented students.The project will propose a novel slow-kill technique for large-scale variable selection, motivated by a scalable optimization algorithm with iteration-varying threshold and simultaneous L2-regularization. The three main elements of progressive quantile control, growing learning rate and adaptive L2-shrinkage in slow kill have solid theoretical support, and its ability to reduce the problem size during the iteration, as opposed to boosting and forward pathwise algorithms, makes it attractive for big data. The interplay between statistics and optimization in the project will reveal tight error rates and fast convergence under some regularity conditions, without the need to pursue a globally optimal solution. Furthermore, a framework of outlier-resistant estimation will be introduced to robustify a given method beyond the standard likelihood setup. It has a close connection to the method of trimming but includes explicit outlyingness parameters for all samples, which in turn facilitates computation and theory. With slow kill, the number of data resamplings will be substantially reduced, and the obtained resistant estimators can enjoy minimax rate optimality in both low and high dimensions. Overall, the proposed research will create a new-generation high dimensional tool for robust sparse learning that can accommodate coherent designs and gross outliers in big data applications, to deepen and broaden existing methods and theory in statistics and optimization.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.

大数据应用通常涉及大量的样本和特征，并且经常被离群值污染，这对变量选择和参数估计提出了挑战。在实践中，用指定的基数拟合稀疏模型是一个常见的要求，但它与解决高度非凸和离散的问题有关。在这种非凸优化中使用多个起点是常见的，但在大数据上通常是计算上禁止的;需要新的具有成本效益的技术来减轻起点要求并确保最佳的统计准确性。此外，如何调整一个任意给定的损失函数，以防止总的离群值，并实现一个高的崩溃点，现代数据分析提出了一个重大挑战。该项目将研究创新和有效的统计方法，并进行严格的理论分析来回答这些问题。在这个项目中，教育与研究紧密结合，包括课程开发，学生辅导，外展和招募代表性不足的学生。该项目将提出一种新的慢杀技术，用于大规模变量选择，其动机是一种可扩展的优化算法，具有迭代变化的阈值和同步L2正则化。渐进分位数控制、增长学习率和自适应L2收缩在慢杀中的三个主要元素有坚实的理论支持，并且它在迭代过程中减少问题大小的能力，而不是boosting和forward pathwise算法，使其对大数据具有吸引力。该项目中统计和优化之间的相互作用将揭示在某些规则性条件下的严格错误率和快速收敛，而无需追求全局最优解。此外，一个框架的离群抗估计将被引入到robustify一个给定的方法超出标准的似然设置。它与修剪方法有密切的联系，但包括所有样本的显式outlyingness参数，这反过来又有利于计算和理论。通过慢杀，数据重采样的次数将大大减少，并且所得到的抵抗估计量在低维和高维都具有极大极小率最优性。总体而言，拟议的研究将创建一个新一代的高维工具，用于强大的稀疏学习，可以适应大数据应用中的连贯设计和总离群值，以深化和扩大现有的方法和理论在统计和优化。这个奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。