UK: PhD position: Kernel Methods for Randomised Numerical Linear Algebra

Randomised Numerical Linear Algebra (RNLA) underpins scalable algorithms for large-scale matrix computations, including least-squares regression, low-rank approximation, and subspace embedding. Central to these methods is constructing subsampling distributions such as those based on statistical leverage scores, that preserve matrix geometry. However, computing or approximating these distributions efficiently and reliably at scale when exact scores are prohibitively expensive remains a major computational bottleneck.

This project - to start Fall 2027 - will investigate novel connections between RNLA subsampling and kernel-based distribution approximation to develop new theoretical foundations and practical algorithms for constructing compact, representative matrix sketches. Depending on candidate strengths and interest, the research offers scope for both rigorous theoretical contributions such as establishing formal guarantees relating sketch quality to downstream algorithm performance, and computational implementation on large-scale problems.

Sitting at the intersection of numerical linear algebra, approximation theory, and kernel methods, this project advances the foundational algorithms powering modern large-scale data analysis and scientific computing. It is ideal for candidates in Applied Mathematics, Theoretical Computer Science, or Quantitative Engineering with a solid background in linear algebra and probability. Familiarity with randomised algorithms or functional analysis is desirable but optional.

Interested applicants should contact npolydor@ed.ac.uk before January 2027 to discuss funding options.