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

预测建模技术的最新进展通过从过去的事件中提取隐藏的趋势和获得有价值的知识，大大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的一种基本方法，旨在通过利用领域知识、用观察数据制定数学程序和利用计算资源解决问题来产生稳健的结果。例如，如果专家认为数据中有一些部分是不重要的，模型应该能够检测并避免涉及这些数据，以提高预测的准确性。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了哪些测试，则必须有一个精确的模型来再现该结构以供实际应用。通过适当的建模来实现这些期望的条件对于集成先前对问题的理解以及遵守程序和操作限制是至关重要的。该项目旨在通过为许多现有问题引入统一的框架，并通过数学优化方法提供计算工具，扩展具有结构化稀疏性的预测建模的现有知识。利用指示函数的离散性可以精确地表示模型变量中的稀疏模式，利用代理函数可以近似地表示模型变量中的稀疏模式。该项目旨在调查通过将这些条件作为硬性约束来实施的有效性。主要目标包括：1)将现有问题表述为约束优化问题，使模型相对于所提供数据的损失最小化，同时遵守预先确定的稀疏性条件；能够有效处理由此产生的非凸约束的高效鲁棒算法；3)与实践中使用的最新稀疏建模技术相比，研究了新方法的数值性能。基于先前的工作，研究者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性质的平稳解。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，并研究模型在预测精度、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，包括数据和实现的产品，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。

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.