Determinantal Point Processes in Randomized Numerical Linear Algebra

Randomized Numerical Linear Algebra (RandNLA) uses randomness to develop improved algorithms for matrix problems that arise in scientific computing, data science, machine learning, etc. Determinantal Point Processes (DPPs), a seemingly unrelated topic pure and applied mathematics, is class of stochastic point processes with probability distribution characterized by sub-determinants kernel matrix. Recent work has uncovered deep fruitful connections between DPPs RandNLA which lead new guarantees are interest both areas. We provide an overview this exciting line research, including brief introductions DPPs, as well applications classical linear algebra tasks such least squares regression, low-rank approximation the Nystrom method. For example, random sampling DPP leads kinds unbiased estimators squares, enabling more refined statistical inferential understanding these algorithms; is, some sense, optimal randomized algorithm method; technique called leverage score can be derived marginal DPP. also discuss recent algorithmic developments, illustrating that, while not quite efficient standard techniques, DPP-based only moderately expensive.