CRII: III: Learning Predictive Models with Structured Sparsity: Algorithms and Computations

CRII：III：学习具有结构化稀疏性的预测模型：算法和计算

• 批准号: 1948341
• 负责人: Miju Ahn
• 金额: $ 13.2万
• 依托单位: Southern Methodist 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=1948341&HistoricalAwards=false
• 关键词: CRII; III; Learning; Predictive; Models

Recent advances in predictive modeling technology have greatly reinforced human decision-making processes by extracting hidden trends and gaining valuable knowledge from the past events. Predictive modeling for sparse representation is a fundamental methodology in machine and statistical learning that aims to produce robust outcomes by exploiting domain knowledge, formulating mathematical programs with observed data, and solving the problems with computational resources. For example, if experts believe there are some parts of data that are insignificant, the model should be able to detect and avoid involving such data to increase prediction accuracy. If features of the data possess hierarchical relationships, e.g.,availability of medical measurements depends on which tests were given to the patient, an accurate model must reproduce the structure for practical applications. Achieving such desired conditions through proper modeling is critical to integrate prior understandings of the problem, and adhere to procedural and operational restrictions. This project aims to expand current knowledge of predictive modeling with structured sparsity by introducing a unified framework for many existing problems and providing computational tools through mathematical optimization methodologies.The sparse patterns in the model variables can be formulated exactly by utilizing the discrete property of the indicator function, and approximately by using surrogate functions. The project aims to investigate effectiveness of imposing such conditions by enforcing them as hard constraints. The main objectives include 1) formulating existing problems as constrained optimization problems, which minimizes the model's loss with respect to the provided data while obeying pre-determined sparsity conditions, 2) developing e;fficient and robust algorithms that are capable of effectively handling resulting nonconvex constraints, and 3) studying numerical performance of the new method compared to the latest sparse modeling technologies used in practice. Based on the prior work, the investigator aims to develop deterministic and randomized algorithms that compute stationary solutions with desirable theoretical properties through iterative procedures. Specific research tasks include implementing the proposed method applied to simulated and real data, and investigating robustness of the model in terms of prediction accuracy, ability to identify significant components of data, and successful reproduction of desired sparse patterns in the repeated experiments. The outcome of this project including data and implemented products will be shared with the public through open-source communities and online repositories.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.

预测建模技术的最新进展通过提取隐藏的趋势并从过去的事件中获取有价值的知识，极大地加强了人类的决策过程。稀疏表示的预测建模是机器和统计学习中的一种基本方法，旨在通过利用领域知识、利用观察到的数据制定数学程序以及利用计算资源解决问题来产生稳健的结果。 例如，如果专家认为数据的某些部分不重要，则模型应该能够检测并避免涉及此类数据，以提高预测准确性。如果数据的特征具有层次关系，例如，医学测量的可用性取决于对患者进行的测试，则准确的模型必须重现实际应用的结构。通过适当的建模实现此类所需条件对于整合对问题的先前理解并遵守程序和操作限制至关重要。该项目旨在通过引入针对许多现有问题的统一框架并通过数学优化方法提供计算工具来扩展当前对结构化稀疏性预测建模的知识。利用指标的离散特性可以精确地制定模型变量中的稀疏模式函数，并且近似地通过使用代理函数。该项目旨在通过强制实施这些条件作为硬性约束来调查施加这些条件的有效性。主要目标包括 1) 将现有问题表述为约束优化问题，从而在遵守预定稀疏条件的同时最大限度地减少模型相对于所提供数据的损失，2) 开发高效且稳健的算法，能够有效处理由此产生的非凸约束条件；3）研究新方法与实践中使用的最新稀疏建模技术的数值性能。基于之前的工作，研究人员的目标是开发确定性和随机算法，通过迭代过程计算具有理想理论特性的平稳解。具体的研究任务包括将所提出的方法应用于模拟和真实数据，并研究模型在预测准确性、识别数据重要组成部分的能力以及在重复实验中成功再现所需稀疏模式方面的鲁棒性。该项目的成果（包括数据和实施的产品）将通过开源社区和在线存储库与公众共享。该奖项反映了 NSF 的法定使命，并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，被认为值得支持。

项目成果

A Cardinality Minimization Approach to Security-Constrained Economic Dispatch

安全约束经济调度的基数最小化方法

• DOI: 10.1109/tpwrs.2021.3133379
• 发表时间: 2021-12
• 期刊: IEEE Transactions on Power Systems
• 影响因子: 6.6
• 作者: Troxell, David;Ahn, Miju;Gangammanavar, Harsha
• 通讯作者: Gangammanavar, Harsha

Iteratively Reweighted Group Lasso Based on Log-Composite Regularization

基于对数复合正则化的迭代重加权群套索

• DOI: 10.1137/20m1349072
• 发表时间: 2021-01
• 期刊: SIAM Journal on Scientific Computing
• 影响因子: 3.1
• 作者: Ke, Chengyu;Ahn, Miju;Shin, Sunyoung;Lou, Yifei
• 通讯作者: Lou, Yifei