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

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.