CDS&E-MSS: Optimal Recovery in the Age of Data Science

机器学习技术已经被证明是成功的，它将社会带入了一个由数据科学增强的现代时代。这些技术通常依赖于统计假设，提供的解决方案保证在大多数情况下都能很好地工作。然而，这些假设和限制不足以满足对美国至关重要的领域的需求，如国防、医药和运输。在这些应用程序中，失败（尽管很少发生）是不可避免的。该项目侧重于具有在最坏情况下有效的认证保证的数据科学算法。它的理论结果将对任何涉及随机模型无法捕获的数据的科学领域产生影响。学生将参与研究并接受下一代数据科学工具的培训。该项目将在近似理论的一个子领域内开发称为最优恢复的方法，重点是提高其计算实用性，而不是抽象理论。特别是，纯粹的分析方法将被利用现代优化理论的更具计算性的观点所取代。另一个与传统理论的突破在于对现实世界的函数进行建模，不是通过它们的平滑性，而是通过它们的近似性，这与数值方法相关，例如基于神经网络的方法。该项目有几个方面：理论方面扩大了最佳采收率的范围，以确保现代数据科学所需的体积、准确性、速度和多样性的特性；计算方面，包括将恢复方法实现为公开可用的高效算法；一个实际的方面，包括在应用领域，如在系统识别转移理论发现；教育方面包括将新概念融入下一代的科学文化中。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。

Machine learning techniques have proved to be successful, leading society to a modern era enhanced by data science. These techniques usually rely on statistical assumptions and provide solutions that are guaranteed to work approximately well most of the time. However, these assumptions and limitations are insufficient to meet the demands of areas critically important to the Unites States, such as defense, medicine, and transportation. In these applications a failure, however infrequent, is not an option. This project focuses on data science algorithms with certified guarantees valid in a worst-case setting. Its theoretical outcomes will have implications in any field of science involving data not favorably captured by random models. Students will be involved in research and receive training in next generation data science tools. The project will develop methods within a subfield of approximation theory called Optimal Recovery with focus on improving their computational practicality rather than on abstract theory. In particular, purely analytic approaches will be replaced by a more computation-embracing perspective exploiting modern optimization theory. Another breakaway from traditional theory consists in modeling real-world functions not by their smoothness properties but by their approximability properties which is relevant for numerical approaches, e.g., those based on neural networks. The project has several facets: a theoretical facet expanding the scope of optimal recovery to ensure the properties of volume, veracity, velocity, and variety which are desirable in modern data science; a computational facet that consists in implementing recovery methods as efficient algorithms made publicly available; a practical facet that consists in transferring the theoretical findings in applied fields such as in system identification; and an educational facet that consists in integrating novel concepts into the culture of the next scientific generation.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.