Collaborative Research: Randomized Numerical Linear Algebra for Large Scale Inversion, Sparse Principal Component Analysis, and Applications

Emory University, Atlanta GA

Investigators

Abstract

In many scientific applications such as genetics, geophysics, bioinformatics, and medicine, data are being generated at ever-increasing rates. For these, and other data-intensive applications, the massive size of the data sets, as well as the growing model complexities, present fundamental computational challenges. State-of-the-art inference methods have exceeded their limits of applicability and advanced mathematical, computational, and statistical tools are urgently needed to extract relevant information. This research addresses the urgent need to advance efficient methods for computing solutions of large-scale inverse problems. This project will advance tools from inverse problems which will be merged with novel approaches from randomized numerical linear algebra, and sparse principal component analysis. The expanded tools produced by this project will have the ability to transform the field of large-scale inverse problems and subsequently benefit a wide variety of applications. The development of novel approaches for large-scale inversion will significantly advance current solutions in a wide range of applications, such as machine learning, geophysics, and genetics. This project will investigate advanced iterative methods for inverse problems, randomization, sketching schemes, as well as methods for sparse principal component analysis. By accelerating numerical methods, providing theoretical convergence analysis, and producing a user-friendly software package, the broader scientific community will be able to integrate these advanced tools within their application areas. The project offers training opportunities for students in computational and applied mathematics. These include the implementation of a novel cross-institutional graduate course, merging the expertise of the three PIs in the topics of inverse problems, randomized linear algebra, and numerical optimization, to provide a broader opportunity for graduate students to engage in timely research projects; connect with their peers across the US; and expand the diversity pool of students in our programs. Collaborations between the project team and domain experts guarantee that the proposed algorithms and software will have an impact on real data. 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.