The growing extent of problem complexity and the increasing amount of data in data science projects often result in computation of high-dimensional matrix operations, which have posed great challenges on the computational capabilities. One example is the optimization problems that arise in system identification based on Gaussian process regression.
On the other hand, a class of rank-structured matrices can be stored much more efficiently than general dense matrices, which we often directly obtain from data preprocessing, and by exploiting their inherent structure, many computational operations can be accelerated.
This project concerns the detection and use of rank structure in optimization problems in some interesting applications. However, rank structure can be difficult to expose, and computing a rank-structured approximation to a general matrix that is constructed from data often poses a computational bottleneck. To overcome both challenges, this project will propose and investigate various detection strategies and develop new, computationally efficient approximation methods. Meanwhile, due to the specific requirements of some problems, some key properties need to be preserved. For example, system ID problem requires symmetry and/or positive definiteness of the matrices.
The outcome of the project will be a set of building blocks that can be used to construct scalable methods for system identification as well as other applications within data science where rank structure is either intrinsic or provides a good approximation.