CIF: Small: Precise Computational and Statistical Tradeoffs for Iterative Signal Estimation and Supervised Learning

由于新型传感器和采集设备的激增，从医学成像到在线广告等许多现代应用中收集了大量数据集。传统的统计信号估计和机器学习理论旨在了解数据分析算法的预测能力或准确性如何随数据大小而变化。然而，考虑到现代数据集的庞大规模，这些经典的统计理论是不够的，因为算法必须在各种新的约束下有效地运行，例如有限的处理时间、固定的计算预算和通信约束。该项目旨在开发统计准确性如何与这些资源约束相权衡的基本限制，以及几乎达到此类性能限制的算法。由此产生的信号估计和学习算法被部署在新的应用中，旨在减少医学成像设备的采集时间，并加速其他数据处理领域的并行算法。该项目的部分内容将被整合到高级研究生课程中，精选结果将用于激励K-12学生追求STEM（科学，技术，工程和数学）的职业生涯。在这个项目中，研究小组研究了一组用于信号估计和无监督学习的凸优化算法。该项目的主要目标是了解迭代凸优化算法的统计性能如何与各种统计和计算资源（如运行时间、数据大小、通信等）进行权衡。理论研究利用凸分析、概率论和信息论的技术。理论分析可用于建立流行的凸优化问题的基本性能界限，并指导新算法的设计，以实现竞争资源约束之间的最佳权衡。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。

Due to the proliferation of new sensors and acquisition devices, massive data sets are gathered in many modern applications ranging from medical imaging to online advertisement. Conventional statistical signal estimation and machine learning theory aims to understand how the predictive ability or accuracy of data analysis algorithms scales with data sizes. However, given the sheer size of modern data sets, these classical statistical theories are insufficient as algorithms have to operate effectively under a variety of new constraints such as, limited processing time, fixed computational budget and communication constraints. This project aims to develop the fundamental limits of how statistical accuracy tradeoffs with these resource constraints together with algorithms that nearly achieve such performance limits. The resulting signal estimation and learning algorithms are deployed in novel applications aimed at decreasing the acquisition time in medical imaging devices and speeding up parallelized algorithms in other data processing domains. Parts of this project are integrated into an advanced graduate class and select results will serve to motivate K-12 students to pursue careers in STEM (Science, Technology, Engineering and Math). In this project, the team of researchers study a family of convex optimization algorithms used for signal estimation and unsupervised learning. The main goal of this project is to understand how the statistical performance of iterative convex optimization algorithms tradeoffs with various statistical and computational resources such as run time, data size, communication, etc. The theoretical investigations utilizes techniques from convex analysis, probability, and information theory. The theoretical analysis can be used to establish fundamental performance bounds for popular convex optimization problems and guide the design of new algorithms that achieve optimal trade-offs between competing resource constraints.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.