The Department of Applied Mathematics weekly seminar is given by scholars and researchers working in applied mathematics, broadly interpreted.
Title: Everything is Vecchia: Unifying low-rank and sparse inverse Cholesky approximations
Abstract. The partial pivoted Cholesky approximation accurately represents matrices that are close to being low-rank. Meanwhile, the Vecchia approximation accurately represents matrices with inverse Cholesky factors that are close to being sparse. What happens if a partial Cholesky approximation is combined with a Vecchia approximation of the residual? Our work shows how the sum is exactly a Vecchia approximation of the original matrix with an augmented sparsity pattern. Thus, the Vecchia approximation subsumes a class of existing matrix approximations and has broad applicability.